а) The relation R on A = {3, 5, 7, 9} is defined by the ordered pairs below: R= {(3, 3), (3, 9), (5, 3), (5, 7), (7, 3), (7, 9), (9, 3), (9, 5), (9, 9)} Does the relation R have reflexive, irreflexive, symmetric, asymmetric, antisymmetric or transitive properties? Give a counterexample if the answer is “No".

Q: • if Rit is a symmetrical relationship then R-1 is not symmetrical False O true نقطة واحدة • ifA =…

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Q: R and S are relations on set A = {1,2,3,4}, defined as R = {(1,2},(1,3),(2,3),(2,4),(3,1)}; S =…

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Q: Let A = {1,2,3,4} and B = {5, 6, 7}. Let f be the relation f = {(1,5). (2,5), (3,6), (?, ?)} where…

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Q: Let A be the towns {P, Q, R, S}. Let B be the one way street relation {(P, S), (Q, P), (R, P), (S,…

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Q: Let ∼be the relation on Z defined as follows: For every m, n ∈Z, m ∼n if, and only if, 5 | (m2 −n2…

A: (a) For every m ∈ Z, 5 | (m2 −m2) = 0      Hence, m ~ m for all m ∈ Z      Hence, ~ is reflexive.

Q: Which of these relations on the set {0, 1, 2, 3} are equivalence relations? Determine the…

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Q: Q4) Find the following: 1- Find the relation Z from C to X where C = {1, 2, 3, 5} and X = {4, 6, 9}.…

A: Here, C=1,2,3,5X=4,6,9

Q: 11. Let R₁ and R₂ be the relations on {1,2,3,4} given by R₁ = {(1,1), (1,2), (3,4), (4,2)) R₂ =…

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Q: Suppose that f : A → B is a function, viewed as a relation (set of ordered pairs). Let f* denote the…

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Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

Q: Let R be an equivalence relation on A = {0, 1, 4, 5, 7, 9} and R = {(0, 9), (9, 0), (0, 0), (9, 9),…

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Q: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

Q: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

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Q: Let R=}(x,y)|2 divides 8x+by} be a relation the Set H= {1, 2,3.4,5, 6. 10 Determine whether the…

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Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

Q: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: Given 0,0,1,1,1,2,2,1,2,2,3,2

Q: Identify the directed graph that represents the relation {(a, a), (a, b), (b, c), (c, b), (c, d),…

A: We need to identify the directed graph that represents the relation {(a, a), (a, b), (b, c), (c, b),…

Q: What are the equivalence classes of the equivalence relations on {0, 1, 2, 3}?

A: Answer:-  Find the equivalence classes of the equivalence relations on A = {0, 1, 2, 3}?

Q: PROBLEM 7 art 1. The drawing below shows a Hasse diagram for a partial order on the set A, B, C, D,…

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Q: Which relation on the set {a, b, c, d} are equivalence relations and contain (i) (b, c) and (c, d)…

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Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

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Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: 1. Consider the relationR =…

A: In mathematics, the reflexive closure of a binary relation R on a set X is the smallest reflexive…

Q: What is the composite

A: Let A,B and C be three sets. Suppose that R is a relation from A to B, and S is a relation from B to…

Q: How many relations are there on the set {a, b}. Show all possible relations on the set {a, b} in…

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Q: Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r,…

A: (a) Obtain the composite relation as follows.

Q: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

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Q: Draw a directed graph (digraph) for the relation on {1,2,3,4} {(1,1), (1,4), (2,2), (3,3), (4,1)

A: From the given relation {(1,1), (1,4), (2,2), (3,3), (4,1)} on {1,2,3,4}, draw a directed graph.…