Unformatted text preview: Y and A ⊂ Y , B ⊂ Y . Prove that (a) f1 ( A ∪ B ) = f1 ( A ) ∪ f1 ( B ), (b) f1 ( A ∩ B ) = f1 ( A ) ∩ f1 ( B ). 7. Let X and Y be ﬁnite sets with m elements in X and n elements in Y . (a) How many functions are there from X to Y ? (b) How many injections are there from X to Y ? (c) How many bijections are there from X to Y ? 8. Prove that (a) ( ∀ n ∈ N + ) 1 3 + 2 3 + 3 3 + ··· + n 3 = ± n ( n + 1) 2 ² 2 . (b) ( ∀ n ∈ N + ) 1 · 1! + 2 · 2! + 3 · 3! + ··· + n · n ! = ( n + 1)!1. (c) ( ∀ n ∈ N + ) (64  (9 n8 n1)). (d) ( ∀ n ∈ N + ) (19  (5 · 2 3 n2 + 3 3 n1 ))....
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 Winter '10
 Spyros
 Inverse function, 1 g, n+, ∀n ∈ N+

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