Given the sets X = {1,2,3} and Y = {a,b,c, d}. Define relations a, B, y: X Y by a(1) = b,a(2) = d, a(3) = a B(1) = c, B(2) = a, B(3) = c (1) = a, y(2) = d,y(3) = b,7(1) = c Answer True or False. Provide a rationale for every answer.

Q: If A = {1,2,3,4} give an example of a relation R on A that is: Reflexive and symmetric but not…

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Q: {(1, 2), (2, 3), (3, 4)). (Click to select) (Click to select) symmetric none of these properties…

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Q: Let R be the relation {(a, b) | a‡b} on Z. Then, the reflexive closure of Ris

A: The smallest reflexive relation containing the original relation is called the reflexive closure of…

Q: Select one or more: transitive symmetric

A: Given, and Where be a relation on

Q: Let R= {(a, b): 3keza k* b} be a relation over the positive integers. Prove or disprove thatR is a…

A: A relation R is partial order relation if R is reflexive, antisymmetric and transitive.

Q: Let R1 and R2 be two different relations on the same set A. If R1 - R2 is reflexive then R1 is…

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Q: Show that if AB BA, then eA+BeAeB, but if they do commute, then the relations hold

A: The problem concerns exponentials of matrices and commutativity

Q: For each of these relations on the set (1, 2, 3, 4), decide whether it is reflexive, symmetric,…

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Q: let R be the relation on the set of positive integers in which a R b if and only if a is a factor of…

A: Given below the detailed Solution.

Q: (a) x and y are in the same major. (b) x and y have the same last name. (c) x and y are taking a…

A: See the attachment

Q: Let R2 be the relation on Z+ such that rR2y if and only if 2x + y is a multiple of 3. (Recall that…

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Q: Count the number X of functions y: (20, 21,..., 23) → (5,6,...,8) so that is not onto. X =

A: Given function φ:(20,21,...,23)→(5,6,...,8)

Q: If S and R are both anti-symmetric, then S∘R is anti-symmetric. (f) If S is anti-symmetric, then…

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Q: Let R and S be relations defined on the set of {9,3, 1,0}. R = {(1,1), (9, 3), (1,3), (9,0)}. S =…

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Q: Let R1 be the relation on Z+ such that ¤R¡y if and only if ry > 3. (Recall that Z+ = {1,2, 3, 4,…

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Q: From fundamental property relations, proof the following equation is valid. %D | T.

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Q: Let A = {1, 2, 3, 4}. Give an example of a relation on A that is (R = Reflexive, S = Symmetric, T =…

A: (a) Consider the Relation          V = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (2, 3), (3,…

Q: Let R be the relation on a set A = {a, b, c, d} defined by R= {(a, a), (a, b), (b, b), (b, c), (c,…

A: If R is a relation on a set A, then R^2 is the set of ordered pairs (a, c) such that there exists an…