Prob. Let A,B,C be any three sets, then prove that-

Prob. Prove that-

Prob. If A, B, C, D are any four sets then prove that -

Prob. Show that-

(P∩Q)X(R∩S) = (PXR)∩(QXS)

Prob. Show that the relation-

R = {(a,b)| a, b ∈ Z and a - b is divisible by 3}

Is an equivalence relation, where Z is the set of all integers.

Prob. Let R be a binary relation on the set of all integers such that R= {(a, b)|(a - b ) is an even integer}. Is R an equivalence relation?

Prob. Let R be the relation defined on the integers by aRb if a - b is even. Show that R is an equivalence relation.

Prob. Let R be a binary relation on the set of all positive integers such that

R = {(a, b): | a - b | ≤ 1, a, b, are positive integers}.

Is R an equivalence relation ?