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Unformatted text preview: SOLUTIONS  ANALYSIS  MIDSESSIONAL EXAM JANUARY 2008 This paper has two sections, A an B. Please use a separate answer book for each section. Section A has four short questions, ALL of which you should answer. Each of these questions is worth 10 marks. Section B has two longer questions, of which you should answer ONE . Each of these questions is worth 60 marks. The total mark for the paper is 100. Calculators MAY NOT be used in this examination. NOTE: The notation N + stands for the set of all positive integers: N + = { 1 , 2 , 3 ,... } . 1. Short Questions A1. Using a truth table, prove the contrapositive law ( A B ) ( B A ). Solution. [Similar to homework, 10 marks.] We prove the law using the following truth table. A B A B A B B A ( A B ) B A T T F F T T T T F F T F F T F T T F T T T F F T T T T T A2. Let A , B , C be sets. Prove that A ( B C ) = ( A B ) ( A C ) . Solution. [Similar to homework, 10 marks.] { x A ( B C ) } { x A ( x B C ) } { ( x A ) [ ( x B ) ( x C )] } { [( x A ) ( x B )] [( x A ) ( x C )] } { ( x A B ) ( x A C ) } { x ( A B ) ( A C ) } ....
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 Fall '08
 IvorMcGillivray

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