Relation

Prob. Let A,B,C be any three sets, then prove that-
AX(BC) = (AXB) (AXC)
Solution: Click here.


Prob. Prove that-
A(BC) = (AB) (AC)
Solution: Click here.


Prob. If A, B, C, D are any four sets then prove that -
(AB)X(CD) = (AXC)(BXD)
Solution: Click here.


Prob. Show that-
(PQ)X(RS) = (PXR)(QXS)
For some arbitrary sets P, Q, R and S.
Solution: Click here.


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 ?

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