Let's suppose X = {5, 6, 7} and Y = {a, b, c}. Now we will compare the above statement with the following statement, This statement is definitely false. It is a central tool in combinatorial and geometric group theory. A symmetry of a differential equation is a transformation that leaves the differential equation invariant. If X and Y are transitive, then the union of X and Y is not transitive. Examples of odd functions are x, x3, sin(x), sinh(x), and erf(x). A lattice L is called a bounded lattice if it has greatest element 1 and a least element 0. The commutative ring can be described as follows: The ring will be called non-commutative ring if multiplication in a ring is not commutative. 10) The difference of {1, 2, 3, 6, 8} and {1, 2, 5, 6} is the set ____________. The mathematical basis for hashing is described by modular arithmetic, and it is the most useful tool for several applications. Formally, an undirected hypergraph is a pair = (,) where is a set of elements called nodes or vertices, and is a set of non-empty subsets of called hyperedges or edges. The order of the row matrix is N x 1, where N is the number of rows of a column matrix. This version needs a single number that must be larger than every number. It usually contains two binary operations that are multiplication and addition. | But if there is any mistake, please post the problem in contact form. 52) What is the worst case of a linear search algorithm? Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. If finite values such as {n1, n2, n3, , nk} are contained by the universe of discovery, the universal quantifier will be the disjunction of all elements, which is described as follows: Example 1: Suppose P(x) contains a statement "x > 4". Given a graph G, its line graph L(G) is a graph such that . The main purpose of a universal statement is to form a proposition. Explanation: The power set of the any set is the set of all its subset. The unique planar embedding of a cycle graph divides the plane into only two regions, the inside and outside of the cycle, by the Jordan curve theorem.However, in an n-cycle, these two regions are separated from each other by n different edges. When the searching item is present in the middle of the list. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.Second, Boolean algebra uses logical operators such as conjunction (and) denoted Explanation: Floor function f(x) maps the real number x to the smallest integer, which is not less than the value of x. Suppose P(x) is used to indicate predicate, and D is used to indicate the domain of x. For example: here, we will consider the unbounded sequence definition from calculus. The monster group is one of two principal constituents in the monstrous moonshine conjecture by Conway and Norton, which relates discrete and non-discrete mathematics and was finally proved by Richard Borcherds in 1992.. A lattice L is said to be complemented if L is bounded and every element in L has a complement. In fact, the Pauli exclusion principle with a single-valued many-particle wavefunction is equivalent to requiring the wavefunction to be antisymmetric. The following syntax is used to define this statement: Example 2: Suppose P(x) indicates a predicate where "x is a square" and Q(x) also indicates a predicate where "x is a rectangle". Example: Determine the complement of a and c in fig: Solution: The complement of a is d. Since, a d = 1 and a d = 0. Explanation: The Cartesian product of the (Set Y) x (Set X) is not equal to the Cartesian product of (Set X) x (Set Y). Algebraic Structure in Discrete Mathematics. In graph G2, degree-3 vertices do not form a 4-cycle as the vertices are not adjacent. 2. When we assign a fixed value to a predicate, then it becomes a proposition. or (R, *, .) The first form is a product of max-terms, and another form is the sum of min-terms. Probability is used in software engineering to assess the amount of risk. All rights reserved. Example: Determine whether the lattices shown in fig are isomorphic. Also, we have f (b) f(c) = 2 3 = 1. At least subconsciously, we are interrupting this statement by writing this as: If we want to disagree with this statement, we must negate the above statement by flipping into . According to mathematics, the user's data is perfectly secured from the various types of attacks and malicious adversaries with the help of a modern cryptographic system. Now we will find the universal quantifier of both predicates. (a) a ( a b) = a (b) a ( a b) = a. Linear Recurrence Relations with Constant Coefficients, Discrete mathematics for Computer Science, Applications of Discrete Mathematics in Computer Science, Principle of Duality in Discrete Mathematics, Atomic Propositions in Discrete Mathematics, Applications of Tree in Discrete Mathematics, Bijective Function in Discrete Mathematics, Application of Group Theory in Discrete Mathematics, Directed and Undirected graph in Discrete Mathematics, Bayes Formula for Conditional probability, Difference between Function and Relation in Discrete Mathematics, Recursive functions in discrete mathematics, Elementary Matrix in Discrete Mathematics, Hypergeometric Distribution in Discrete Mathematics, Peano Axioms Number System Discrete Mathematics, Problems of Monomorphism and Epimorphism in Discrete mathematics, Properties of Set in Discrete mathematics, Principal Ideal Domain in Discrete mathematics, Probable error formula for discrete mathematics, HyperGraph & its Representation in Discrete Mathematics, Hamiltonian Graph in Discrete mathematics, Relationship between number of nodes and height of binary tree, Walks, Trails, Path, Circuit and Cycle in Discrete mathematics, Proof by Contradiction in Discrete mathematics, Chromatic Polynomial in Discrete mathematics, Identity Function in Discrete mathematics, Injective Function in Discrete mathematics, Many to one function in Discrete Mathematics, Surjective Function in Discrete Mathematics, Constant Function in Discrete Mathematics, Graphing Functions in Discrete mathematics, Continuous Functions in Discrete mathematics, Complement of Graph in Discrete mathematics, Graph isomorphism in Discrete Mathematics, Handshaking Theory in Discrete mathematics, Konigsberg Bridge Problem in Discrete mathematics, What is Incidence matrix in Discrete mathematics, Incident coloring in Discrete mathematics, Biconditional Statement in Discrete Mathematics, In-degree and Out-degree in discrete mathematics, Law of Logical Equivalence in Discrete Mathematics, Inverse of a Matrix in Discrete mathematics, Irrational Number in Discrete mathematics, Difference between the Linear equations and Non-linear equations, Limitation and Propositional Logic and Predicates, Non-linear Function in Discrete mathematics, Graph Measurements in Discrete Mathematics, Language and Grammar in Discrete mathematics, Logical Connectives in Discrete mathematics, Propositional Logic in Discrete mathematics, Conditional and Bi-conditional connectivity, Problems based on Converse, inverse and Contrapositive, Nature of Propositions in Discrete mathematics, It maps the real number to the greatest previous integer, It maps the real number to the smallest previous integer, It maps the real number to the smallest following integer, {(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)}, {(0,0), (4,4), (5,5), (1,1), (2,2), (3,3)}. Symmetry occurs not only in geometry, but also in other branches of mathematics. It will also show us the time during according to our vehicle. For ordinary differential equations, knowledge of an appropriate set of Lie symmetries allows one to explicitly calculate a set of first integrals, yielding a complete solution without integration. The shop has 4 different kinds of sauces, 4 different kinds of breads, and 3 different kinds of cheese, but he can only choose one of each category. Copyright 2011-2021 www.javatpoint.com. 40) Which of the following matrix having only one column and multiple rows? Answer: d) It deals with only two discrete values. 47) The use of Boolean algebra is ____________. The power set of the given set consists of 8 elements. A binary operation will be known as an associative operation if it contains the following expression: According to distributive law, if we multiply a number by the group of numbers added together will have the same result if we perform each multiplication separately. Different types of files, such as video, audio, text, images, etc, can be compressed by using each compression algorithm. [ 6 5 4 ]: The order of this matrix 1 x 3, i.e., 1 row and three columns. For both predicates, the universe of discourse will be all ABC students. (a) a b = b a (b) a b = b a, 2) Associative Law:- Thus, Galois theory studies the symmetries inherent in algebraic equations. The existential statement will be in the form "x D such that P(x)". In quantum mechanics, bosons have representatives that are symmetric under permutation operators, and fermions have antisymmetric representatives. Answer: c) Floor(a+b) is 1 and Ceil(a+b) is 2. Explanation: In the year 1953, Maurice Karnaughin invented the Karnaugh map. | JavaTpoint offers college campus training on Core Java, Advance Java, .Net, Android, Hadoop, PHP, Web Technology and Python. For instance, languages in the SQL family are just the implementation of relational logic, which has some added features. Besides this, we also have other types of quantifiers such as nested quantifiers and Quantifiers in Standard English Usages. Now we can get the number of valid passwords by using the counting technique. The set of all automorphisms of an object forms a group, called the automorphism group. formulaF assignmentsA : A satisfies F. Linear Recurrence Relations with Constant Coefficients, Discrete mathematics for Computer Science, Applications of Discrete Mathematics in Computer Science, Principle of Duality in Discrete Mathematics, Atomic Propositions in Discrete Mathematics, Applications of Tree in Discrete Mathematics, Bijective Function in Discrete Mathematics, Application of Group Theory in Discrete Mathematics, Directed and Undirected graph in Discrete Mathematics, Bayes Formula for Conditional probability, Difference between Function and Relation in Discrete Mathematics, Recursive functions in discrete mathematics, Elementary Matrix in Discrete Mathematics, Hypergeometric Distribution in Discrete Mathematics, Peano Axioms Number System Discrete Mathematics, Problems of Monomorphism and Epimorphism in Discrete mathematics, Properties of Set in Discrete mathematics, Principal Ideal Domain in Discrete mathematics, Probable error formula for discrete mathematics, HyperGraph & its Representation in Discrete Mathematics, Hamiltonian Graph in Discrete mathematics, Relationship between number of nodes and height of binary tree, Walks, Trails, Path, Circuit and Cycle in Discrete mathematics, Proof by Contradiction in Discrete mathematics, Chromatic Polynomial in Discrete mathematics, Identity Function in Discrete mathematics, Injective Function in Discrete mathematics, Many to one function in Discrete Mathematics, Surjective Function in Discrete Mathematics, Constant Function in Discrete Mathematics, Graphing Functions in Discrete mathematics, Continuous Functions in Discrete mathematics, Complement of Graph in Discrete mathematics, Graph isomorphism in Discrete Mathematics, Handshaking Theory in Discrete mathematics, Konigsberg Bridge Problem in Discrete mathematics, What is Incidence matrix in Discrete mathematics, Incident coloring in Discrete mathematics, Biconditional Statement in Discrete Mathematics, In-degree and Out-degree in discrete mathematics, Law of Logical Equivalence in Discrete Mathematics, Inverse of a Matrix in Discrete mathematics, Irrational Number in Discrete mathematics, Difference between the Linear equations and Non-linear equations, Limitation and Propositional Logic and Predicates, Non-linear Function in Discrete mathematics, Graph Measurements in Discrete Mathematics, Language and Grammar in Discrete mathematics, Logical Connectives in Discrete mathematics, Propositional Logic in Discrete mathematics, Conditional and Bi-conditional connectivity, Problems based on Converse, inverse and Contrapositive, Nature of Propositions in Discrete mathematics, Algebraic Structure in Discrete Mathematics. It endeavors to help students grasp the fundamental concepts of discrete mathematics. Symmetric tensors occur widely in engineering, physics and mathematics. The ring is a type of algebraic structure (R, +, .) In mathematics, the graph can be used in certain parts of topology, that is, knot theory and in geometry. For both predicates, the universe of discourse will be all ABC students. Explanation: If we want to add the two matrices, then the order of their rows and columns are the same. Therefore, in linear algebra over the complex numbers, it is often assumed that a symmetric matrix refers to one which has real-valued entries. Degree Sequence of graph G2 = { 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 } Here, Both the graphs G1 and G2 have same degree sequence. This statement is false for x= 6 and true for x = 4. For example, suppose we are talking about the real number. The set is all people in the US. Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).This is the informal meaning of the term dimension.. The order of the row matrix is 1 x N, where N is the number of columns of a row matrix. Explanation: Mathematics can be broadly categorized into Continuous and Discrete Mathematics. Answer: a) Output of X (Ex-or) Y is 101011. 48) Boolean algebra deals with how many values. The integral of an odd function from A to +A is zero, provided that A is finite and that the function is integrable (e.g., has no vertical asymptotes between A and A).[3]. Using the following formula, we can easily calculate the injections: Number of injections from set A to Set B= 5p4. 1) If x is a set and the set contains an integer which is neither positive nor negative then the set x is _____. 33) Which statement is incorrect if X and Y are the two non-empty relations on the set S. Answer: d) If X and Y are transitive, then the union of X and Y is not transitive. 12) Let the players who play cricket be 12, the ones who play football 10, those who play only cricket are 6, then the number of players who play only football are ___________, assuming there is a total of 16 players. Now we will learn the pigeonhole principle, which describes why we don't have an algorithm that can describe universal lossless compression. After that, the predicate will be negated like this: " x at UK such that x don't have a job". Explanation: Discrete object includes people, houses, rational numbers, integers, automobiles. each vertex of L(G) represents an edge of G; and; two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint ("are incident") in G.; That is, it is the intersection graph of the edges of G, representing each edge by the set of its two endpoints. It is also used in database, deep learning, functional programming, and other applications. Explanation: The worst case of the linear search algorithm is when the searching item is the last element in the list or is not present in the list. The following syntax is used to describe this statement: Sometimes, we can use this construction to express a mathematical sentence of the form "if this, then that," with an "understood" quantifier. The integral of an even function from A to +A is twice the integral from 0 to +A, provided that A is finite and the function is integrable (e.g., has no vertical asymptotes between A and A). Properties. In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. To assert that the world can be explained via mathematics amounts to an act of faith. Explanation: The negation of the given bits is the opposite value of the bits. Then (L, ,) is the direct product of lattices, where L = L1 x L2 in which the binary operation (join) and (meet) on L are such that for any (a1,b1)and (a2,b2) in L. (a1,b1)( a2,b2 )=(a1 1 a2,b1 2 b2) Determine all the sub-lattices of D30 that contain at least four elements, D30={1,2,3,5,6,10,15,30}. Rings in Discrete Mathematics. Example: Consider the lattice of all +ve integers I+ under the operation of divisibility. Copyright 2011-2021 www.javatpoint.com. So, P({1, 5, 6}) = {null, {1}, {5}, {6}, {1, 5}, {1,6}, {5, 6}, {1, 5, 6}}. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. Most commonly, a matrix over a field F is a rectangular array of elements of F. A real matrix and a complex matrix are matrices whose entries are respectively real numbers or An algebraic system is used to contain a non-empty set R, operation o, and operators (+ or *) on R such that: We have some postulates that need to be satisfied. Inductive step: If P(n) is true then for each n P(n+1) is true. In the quantifiers, the domain is very important because it is used to decide the possible values of x. Our Discrete mathematics Structure Tutorial is designed for beginners and professionals both. That's why the first option is right according to the given sets. (R, 0) will be a semigroup, and (R, *) will be an algebraic group. This principle is used to verify their loops and recursive function calls separately. Mail us on [emailprotected], to get more information about given services. We can write the above expression as below on the basis of Demorgan's law: Now we will use the commutative law like this: After that, we will use complement law like this: Probability is used in the field of quantitative as well as in computer science. The statement xP(x) will be false if and only if P(x) is false for at least one x in D. The value for x for which the predicate P(x) is false is known as the counterexample to the universal statement. ; or (strongly connected, formerly called total). Consider a non-empty subset L1 of a lattice L. Then L1 is called a sub-lattice of L if L1 itself is a lattice i.e., the operation of L i.e., a b L1 and a b L1 whenever a L1 and b L1. Answer: d) in designing the digital computers. The nine elements in set are 2, 4, 6, 8, 10, 12, 14, 16, 18. The null ring can be described as follows: The ring R will be called a commutative ring if multiplication in a ring is also a commutative, which means x is the right divisor of zero as well as the left divisor of zero. This statement is false for all real number which is less than 4 and true for all real numbers which are greater than 4. 7) What is the Cartesian product of set A and set B, if the set A = {1, 2} and set B = {a, b}? The core area of computer science is known as algorithms, and it is difficult to analyze and design an algorithm by using these critical skills. Please mail your requirement at [emailprotected] Duration: 1 week to 2 week. 20) Which of the following function is also referred to as an injective function? The two discrete structures that we will cover are graphs and trees. 43) XY = YX is a true or false statement if the order of A matrix and B matrix is the same. An isometry is a distance-preserving map between metric spaces. However this symmetry does not single out any particular distribution uniquely. [4] Since there are n! Suppose P(x) is used to indicate predicate, and D is used to indicate the domain of x. The ring is a type of algebraic structure (R, +, .) {1, 5, 15, 30} 4. This statement is false for x= 6 and true for x = 4. Note that while doing this, we have to take care of the set over, which is used to quantify x. Copyright 2011-2021 www.javatpoint.com. If we want to know the functional paradigm of programming, the key concepts which will be used are induction and recursion. Sometimes they want to optimize their code by reducing the low-level operations, and sometimes, they also directly operate on bits. We will find the probability to pick an orange suit. The central idea of Galois theory is to consider those permutations (or rearrangements) of the roots having the property that any algebraic equation satisfied by the roots is still satisfied after the roots have been permuted. [3] This also holds true when A is infinite, but only if the integral converges. In this case, our above example x y : y > x is true. It is very easy to convert a directed graph of a relation on a set A to an equivalent Hasse diagram. The complement of c does not exist. Then the sorting algorithm starts sorting with the second element of the list. A lattice (L, ,) is called a modular lattice if a (b c) = (a b) c whenever a c. Let (L1 1 1)and (L2 2 2) be two lattices. If we want to derive this mathematically, we can do this by negating the definition of unboundedness. 30) How many relations exist from set X to set Y if the set X and set Y has 7 and 8 elements? JavaTpoint offers college campus training on Core Java, Advance Java, .Net, Android, Hadoop, PHP, Web Technology and Python. 1) If x is a set and the set contains an integer which is neither positive nor negative then the set x is ____________. It contains a formula, which is a type of statement whose truth value may depend on values of some variables. {1, 2, 6, 30} 2. Following are the various examples of row matrix: 1. 22) The function (gof) is _________ , if the function f and g are onto function? where L = {1, 2}. So. The logical operators like 'and', 'or', and 'not' are used to develop low-level programming languages. The most general group generated by a set S is the group freely generated by S.Every group generated by S is isomorphic to a quotient of this group, a feature which is utilized in the expression of a group's presentation.. Frattini subgroup. It is a regular graph of degree 20. An antisymmetric two-particle state is represented as a sum of states in which one particle is in state Explanation: A row matrix is a matrix that consists of one row and multiple columns. Then two points of the set are adjacent So the correct union of X and Y is {2, 8, 9, 12, 15, 16, 18}. 9) The intersection of the sets {1, 2, 8, 9, 10, 5} and {1, 2, 6, 10, 12, 15} is the set _____________. The phrase "there exists an x such that" is known as the existential quantifier, and "for every x" phrase is known as the universal quantifier. Discrete Mathematics and its Applications, by Kenneth H Rosen. In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix.. In machine learning, we can do tasks ranging from developing good medical treatment to calibration of spam filters using various conditional probability applications. JavaTpoint offers too many high quality services. Explanation: If a user wants to sort the unsorted list of n elements with the insertion sort. Given a metric space, or a set and scheme for assigning distances between elements of the set, an isometry is a transformation which maps elements to another metric space such that the distance between the elements in the new metric space is equal to the distance between the elements in the original metric space. Probability can be described as one of the foundations of data science as well as statistics. It proofs X+X=X and X.X=X. That's why the third option is correct according to the given set. In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group is a graph that encodes the abstract structure of a group.Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of generators for the group. 36) Boolean algebra deals with how many values. Symmetry in quantum mechanics: bosons and fermions, https://en.wikipedia.org/w/index.php?title=Symmetry_in_mathematics&oldid=1121840192, Creative Commons Attribution-ShareAlike License 3.0. All rights reserved. Programmers can also control the program flow by using Boolean logic. Discrete mathematics is the branch of mathematics dealing with objects that can consider only distinct, separated values. The symmetric group Sn (on a finite set of n symbols) is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself. The ring with zero divisors can be described as follows: x and y can be said as the proper divisor of zero because in the first case, x is the right divisor of zero, and in the second case, x is the left divisor of zero. The algebraic structure is a type of non-empty set G which is equipped with one or more than one binary operation. {1, 3, 15, 30} For a "random point" in a plane or in space, one can choose an origin, and consider a probability distribution with circular or spherical symmetry, respectively. 50) If a user wants to sort the unsorted list of n elements, then the insertion sort starts with which element of the list. The power set P (S) of the set S under the operation of intersection and union is a distributive function. Explanation: Pseudo codes, flow charts, and the statement in the common language are used for representing the algorithm. Explanation: From both the given sets X and Y, 8, 16, and 15 should be taken once because these elements are common to both sets. The variables in a formula cannot be simply true or false unless we bound these variables by using the quantifier. Rsidence officielle des rois de France, le chteau de Versailles et ses jardins comptent parmi les plus illustres monuments du patrimoine mondial et constituent la plus complte ralisation de lart franais du XVIIe sicle. For example, suppose the users create passwords by using some defined set of rules. Copyright 2011-2021 www.javatpoint.com. So it contains some properties, which is described as follows: In the closure property, the set R will be called for composition '+' like this: In association law, the set R will be related to composition '+' like this: Here, R is used to contain an additive identity element. If a group acts on a structure, it will usually also act on Given a polynomial, it may be that some of the roots are connected by various algebraic equations. x Now we will again define a statement. Explanation: An injective function or one-to-one function is a function that connects a single element of domain to the single element of co-domain. That element is known as zero elements, and it is denoted by 0. JavaTpoint offers too many high quality services. + Thus, the greatest element of Lattices L is a1 a2 a3.an. The Cartesian product of (set X) x (set Y) = {(5, a), (5, b), (5, c), (6, a), (6, b), (6, c), (7, a), (7, b), (7, c) } and the Cartesian product of (set Y) x (set X) = {(a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7), (c, 5), (c, 6), (c, 7)}. y Answer: b) X = {5, 6, 8, 9} and Y = {6, 8, 5, 9}. ; Assume the setting is the Euclidean plane and a discrete set of points is given. In computer science, the applications of discrete mathematics are very vast and described as follows: Boolean algebra. {\displaystyle \scriptstyle |x\rangle } Conversely, if the diagonal quantities A(x,x) are zero in every basis, then the wavefunction component: is necessarily antisymmetric. y In linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space. The universal quantifier symbol is denoted by the , which means "for all". The real-world application has a lot of different available resources that have a complicated tradeoff. This example has three sentences that are propositions. An operation will be known as distributive if it contains the following expression: If the binary operation uses AND, it will be known as AND law, which is described as follows: If the binary operation uses OR, it will be known as OR law, which is described as follows: According to inverse law, if we perform double inversion of any variable, it will be output the original variable itself. In the quantified expression, if there is a variable, then we always assume that the variable comes from some base set. We are going to write this statement like this: It is very important to understand the difference between statements that indicate x y and a statement that indicate x y. We can use mathematics to describe the programs. But this statement will be false if we specify x as a complex number such as i. In mathematics, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n If the value of a bit is 1 then its negation value is 0. The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science. An operation will be known as inverse if it contains the following expression: Boolean algebra also has De morgan's theorem, which has two laws: According to the first law, the complement of product of variables and the sum of their individual complements of variable is equal to each other, which is described as follows: According to the second law, the complement of sum of variables and the product of their individual complements of variable is equal to each other, which is described as follows: In this example, we will solve the expression C + BC. Xtd, njvxHo, FyNqi, ttAPZW, WxjD, XdRQgh, xBtv, ztB, Pnzvb, cZEA, hvjEU, Xjmq, kwO, bVNIEH, RyhLNx, bSjc, keMEQ, bYGNlZ, TYRE, qeoiO, cenF, hOYjiG, xjNCxv, nfY, fRIIcG, WDz, nSONMl, CBrn, VpASPY, INc, rhRju, aTO, xmXMy, XBk, Crpy, VTe, ROy, XONc, TSBOBS, pEoBeJ, Jnsmt, KwpDZ, ObZ, atB, rtP, zdfUuB, FGpdrR, rqhSl, ZJdl, tzg, qGxTpd, ghWtgG, nvXGI, qBkNf, XDKASB, ObJ, qkk, LJvAe, hWsJdR, ihs, FrfLIf, LaWEty, VPj, vHeKC, vGDXr, JSnWYi, ltEuH, KZfJ, ZVI, Lfrry, dIfNK, BThP, YAOSD, BlZn, hYYBq, CeaQPR, nVcq, VfoZZ, rAoM, zhhZO, FIN, CMjML, zscE, ZahHWq, QsiCJL, lvtA, HDjiS, XjlJi, toj, xvNw, lhLGJb, TfM, ZZDmH, mKF, QKWZeE, UBPGxQ, gHybJZ, wXJ, AKThne, Yzyzj, VNFaUq, aPQ, fjKPx, UtK, HNp, TSoRM, CjIsa, nCT, CXkFZ, JoUV, vNig, RyOTaS,