Let R be a relation on {a, b, c, d}) defined as R = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (d, d)}. Show that the relation R is an equivalence relation using relation matrix.

Q: Given a relation, R on A = {a, b, c, d} on as follows: R = {(а, а), (а, b), (а, d), (b, b), (b, с),…

A: Relation as a Matrix: Let A = {a1,a2,a3,.......am} and B = {b1,b2,b3......bn} are two finite sets,…

Q: Select all pairs in the reflexive closure of the relation R, defined on the set A = { a, b, c, d }…

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Q: Let P={{a,b,d},{c,f},{e,g}} be a partition. Write the relation matrix for the implied equivalence…

A: P={{a,b,d},{c,f},{e,g}} . The  equivalence relation is as follows:…

Q: Show that the relation R on ZxZ defined by (a, b) R (c, d) if and only if a + d = b + c is an…

A: To show that the relation R on Z×Z defined by(a, b) R (c, d) if and only if a+ d = b+ c is an…

Q: Let A = {1, 2, 3, 4}. Define a relation R on A: R = {(1, 2), (1, 3), (2, 2), (2, 3), (3, 4), (4, 3)}…

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Q: Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) E…

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Q: Let A = {p , q, r, s, t, u, v}, and let R be the following equivalence relation on A: R = { (p, p)…

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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: Let A = {1, 2,3, 4}. The following relation R is an equivalence relation on A: R=…

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Q: Q-3: a) Let R be a relation on A = {1,2,3,4} such that aRb means |ab| ≤ 1. Find the matrix…

A: (a) It is given that, R be a relation on A = {1, 2, 3, 4} such that aRb ⇔ a-b≤1 We have to find the…

Q: Let R be the relation on the set A = {a1, a2, a3, a4} whose matrix is given by 1 0 1 0 0 1 0 1 1 0 1…

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Q: why is R1 not symmetric but R3 symmetric? the definition of a symmetric relation R on a set A says…

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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…

Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

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: Lex 172,3,4). Consider the relation R on X defined as follows. R = ((1.1), 13), (2,2), (2.4), (3,1),…

A: I have solved both subpart using basic definition of equivalence relation and equivalence class.