Given a set S = {1, 2, 3, 4, 5}, find the equivalence relation on S which generated by the partition{{1, 2}, {3}, {4, 5}}. Draw the graph of the relation.

Let R be the following equivalence relation on the set A = {1, 2, 3, 4, 5, 6}, R = {(1, 1),(2, 2),(3, 3),(4, 4),(5, 5),(6, 6),(1, 2),(2, 1),(2, 3),(3, 2),(1, 3),(3, 1),(5, 6),(6, 5)}. Find the partitions of A induced by R i.e. A/R.

how that R is an equivalence relation, and find all equivalence classes.(a) R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (1, 5), (5, 1), (3, 5), (5, 3), (1, 3), (3, 1)} on {1, 2, 3, 4, 5}(b) R = {(x, y) : 3 divides (x − y)} on R(c) R = {(x, y) : 3 divides (x + 2y)} on Z(d) R = {(x, y) : x and y are both even} on {1, 2, 3, 4, 5}

A = {1, 2, 3, 4} andR = {(1, 1), (1, 2), (2, 1), (2, 2), (3,4), (4, 3), (3, 3), (4, 4)}.Shows that R is an equivalence relation on A hence find partition of A inducedby R.24. let A = {1, 2, 3,4}. Let R & S be an equivalence relations on A given asR = {(1, 1), (1, 2), (2, 1), (2, 2), (3,4), (4, 3), (3, 3), (4, 4)}S= {(1, 1), (2, 2), (3,1), (1, 3), (3, 3), (4, 4)}find partition of A induced by 𝑅−1 ∩ 𝑆−1 , 𝑅−1 , 𝑅 ∩ 𝑆

Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here R is known as _________a.equivalence relationb.symmetric relationc.transitive relation’’d.reflexive relat

f A={1,4,5} and the relation R defined on the set A as aRb if a+b < 6 checkwhether the relation R is an equivalence relation