Assignment 2.pdf - MA2504 Assignment 2 1 Let P(x be the statement x = x 2 If the universe of discourse is the set of integers what are the truth values

Assignment 2.pdf - MA2504 Assignment 2 1 Let P(x be the...

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MA2504 Discrete Mathematics Assignment 2 1. Let P ( x ) be the statement " . x = x 2 " If the universe of discourse is the set of integers, what are the truth values of the following? (a) P (1) (b) P (-1) (c) P(x) x (d) P(x) x 2. In (a) - (e), (I) rewrite the statement formally using quantifiers and variables, and (II) write a negation for the statement. (a) Everybody trusts somebody. (b) Somebody trusts everybody. (c) The number of rows in any truth table equals 2 n for some integer n . (d) Every action has an equal and opposite reaction. (e) There is a prime number between every integer and its double. 3. Let ( ) , , S x y z denote the predicate “ x y z + = ’, ( ) , , P x y z denote “ x y z = ”, and ( ) , L x y denote x y . Let the universe of discourse be the set of all natural numbers. Express the following assertions using the predicates above. (a) For every x and y , there exists a z such that x y z + = . (b) No x is less than 0. (c) For all x , 0 x x + = . (d) There exists an x such that x y y = for all y .
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