7. Suppose that X and Y are disjoint sets and k E Z»o. Prove that the function p:U (P:(X) × Pk-:(Y)) → Pk(XUY) i=0 p(A, B) = AU B is a bijection. Deduce that (“:”) -±(“)(“) m+n т k i=0 for any m, n, k E Z>o.

7. Suppose that X and Y are disjoint sets and k E Z>o. Prove that the function :U(P:(X) × Pk-i(Y)) → Pr(X UY) i=0 p(A, B) = AU B is a bijection. Deduce that (":") -±(")(") m + n n k i=0 for any m, n, k e Z>o.

 

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7. Suppose that X and Y are disjoint sets and k E Z»o. Prove that the function p:U (P:(X) × Pk-:(Y)) → Pk(XUY) i=0 p(A, B) = AU B is a bijection. Deduce that (“:”) -±(“)(“) m+n т k i=0 for any m, n, k E Z>o.
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