suppose, X=Z; the set of all integers. Let us define a relation R on Z by a R b iff a^2=b^2. Prove that R is Reflexsive, symmetric, Transitive check whether it’s antisymmetric or not.

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Answer:A relation R on a set A is an equivalence relation if and … transitive (x = y and y = z implies x = z) properties. 3.2. … Proof. 1 → 2. Suppose a, b ∈ A and aRb. We must show that [a]=[b].