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7. Suppose that X and Y are disjoint sets and k E Z>o. Prove that the function k so:U(P:(X) × x Pk-i(Y)) → Pk(XUY) 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>0.

7. Suppose that X and Y are disjoint sets and k E Z>o. Prove that the function k so:U(P:(X) × x Pk-i(Y)) → Pk(XUY) 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>0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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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