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Unformatted text preview: f : { } → { , 1 } by f ( x ) = 0 and g : { , 1 } → { } by g ( x ) = 0. (d) True. Use proof by contrapositive. 4.36 (a) If f ◦ g = id B , then for every b ∈ B , f ( g ( b )) = ( f ◦ g )( b ) = id B ( b ) = b which shows that f is surjective. (b) If f ( x ) = f ( y ), then x = id A ( x ) = ( g ◦ f )( x ) = g ( f ( x )) = g ( f ( y )) = ( g ◦ f )( y ) = id A ( y ) = y, so f is injective. 4.47 The maps n 7→ 2 n and n 7→ 2 n + 1 are easily veriﬁed to be bijections from set of natural numbers to the set of even numbers and the set of odd numbers, respectively. 1...
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This document was uploaded on 03/25/2011.
 Spring '10
 Math

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