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# mid-term-2009 - Nanyang Technological University Mid-Term...

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Nanyang Technological University Mid-Term Test 2009 MAS 111 Foundations of Mathematics Time Allowed: 1 Hour Instructions to the candidates The examination consists of FIVE (5) problems. Answer all questions. The marks for each question are indicated at the end of each question. All calculations and answers should be accompanied by appropriate explanations.

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Problem 1 1. Show by constructing truth-tables that u ( v w ) and ( u v ) w are not equivalent and that ( u ( v w )) (( u v ) w ) is a tautology. (10 marks) 2. Prove by applying logical equivalences that r ( p q ) is logically equivalent to ( p r ) q . (So do not use truth-tables.) (10 marks) Problem 2 1. Let U = Z be a universal set, P ( x ) be the statement “ x > 1 ”, and Q ( x ) be the statement “ x < 6 ”. (8 marks) Determine which of the following are true and which are false. (1)
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mid-term-2009 - Nanyang Technological University Mid-Term...

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