Let A and B be sets Prove that A B PPA PPBSolutionLet us ass

Let A and B be sets. Prove that A B P(P(A)) P(P(B))

Let us assume that an element a belongs to A

since A is a subset of B, then a will also belongs to B

hence a will also belong to P(A), since a belongs to B, then a will also belongs to B

then we will have P(A) is a subset of P(B)

similarly, if we have a\' belongs to P(A)

since P(A) is subset of P(B)

then a\' will belong to P(B)

the power set will also contain a\' that implies P(P(A)) and a\' will also belong to P(P(B))

Hence we will have P(P(A)) is a subset of P(P(B))