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MAS111_09_assignment_05

# MAS111_09_assignment_05 - NANYANG TECHNOLOGICAL UNIVERSITY...

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NANYANG TECHNOLOGICAL UNIVERSITY MAS 111 FOUNDATION OF MATHEMATICS ASSIGNMENT 5 TUTORIAL DATES: 22, 23, 24/09/09 1. Let p ( x ) and q ( x ) denote the following predicates: p ( x ) : x 3; q ( x ) : x + 1 is odd . If the domain of x consists of all integers, what are the truth values of the following propositions: (a) q (1) (b) ¬ p (3) (c) p (7) q (7) (d) ¬ ( p ( - 5) q ( - 25)) (e) ¬ ( p ( - 5) q ( - 25)) (f) x p ( x ) (g) x q ( x ) 2. Let p ( x, y ) and q ( x, y ) denote the following predicates: p ( x, y ) : x 2 y ; q ( x, y ) : x + 2 < y. If the domains of x and y consist of all real numbers, what are the truth values of the following propositions: (a) q (1 , π ) (b) p ( - 3 , 8) q (1 , 3) (c) p ( 1 2 , 1 3 ) ∨ ¬ q ( - 2 , - 3) (d) ¬ ( p ( - 5 , 74) q (0 . 3 , - 25))

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(e) x y p ( x, y ) (f) x y q ( x, y ) 3. Let p ( x ), q ( x ), r ( x ), s ( x ) and t ( x ) denote the following predicates: p ( x ): x > 0 q ( x ): x is even r ( x ): x is a perfect square s ( x ): x is (exactly) divisible by 4 t ( x ): x is (exactly) divisible by 5 Let the domains of x be the set of integers. (a) Write the following propositions in symbolic form.
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MAS111_09_assignment_05 - NANYANG TECHNOLOGICAL UNIVERSITY...

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