Question

Let A be non-empty set and P(A) be the power set of A. A relation R is defined on P(A) by X R Y⇔X∩Y=X, X,Y∈P(A). Examine whether R is equivalence.

Please answer with full explanation and proper solving. Please!!

Answer 1

Answer:

Since A∩A=A=ϕ for a non empty set A. So the relation R is not reflexive. If A∩A=ϕ then B∩A=ϕ so the solution R is symmetric. If X=1,2,3,4 and A=1,B=2,3 and C=1,4 then A∩A=ϕ, B∩C=ϕ and A∩C=1 Thus ARB, BRC but A is not related C. Hence R is not transitive.