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Unformatted text preview: points which are joined pairwise by line segments. Problem 5. (a) De±ne a bijection between N and Z . (b) De±ne a bijection between N and N × N . Problem 6. Design an state machine to detect the sequences w satisFying the property ( n 1 ( w )-n ( w ) mod 5) &gt; 2, where n 1 ( w ) and n ( w ) denote the number oF 1’s and 0’s in w , respectively. 1 Problem 7. For functions f : A → B and g : B → C , the composition of g and f , written g o f , is the function h : A → C where h ( a ) = g ( f ( a )). (a) Prove that if f and g are bijections, then so is gof . (b) Prove that if f : A → B is a bijection, then there is a bijection e : B → A , such that e o f = I A , where I A : A → A and I A ( a ) = a for all a ∈ A . 2...
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- Spring '11