mathematical induction and proofs with sets. Please help?

prove that the following holds true for n in N

1^3+2^3+....+n^3= {n^2(n+1)^2}/(4)


Let A B and C be sets. prove that (A-B)intersect C= (A intersect C)-B=(A intersect C)-(B intersect C)

Let A be a set. let f:powerset of A-----> powerset of A be defined by f(X)=A-X for all X in powerset A. prove that f is bijective
 
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