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Week 4 Tutorial - x and y each have domain 1 2 3 Find an...

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Concordia University Department of Computer Science & Software Engineering COMP 232/2 Mathematics for Computer Science FALL 2010 Tutorial Problems (Section DD) : Week 4 4-1. Determine the truth value of the statement x y ( x y 2 ) if the universe of discourse for the variables consists of a) the positive real numbers, b) the integers, c) the nonzero real numbers. 4-2. a) Let F ( p, q ) and G ( p, q ) be logical expressions involving only the proposi- tional variables p and q . Rewrite the statement F ( p, q ) G ( p, q ) using quantifiers and logical operators but not using the symbol. b) Let the variables
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Unformatted text preview: x and y each have domain { 1 , 2 , 3 } . Find an expression with no quantifiers that is logically equivalent to ∀ x ∃ y P ( x, y ) . 4-3. Taking the domain of x , y , and z to be the real numbers, match each of the statements (a) through (e) on the left with a logically equivalent statement on the right. a) ∀ y ( ( x-z ) y 6 = 1 ) 1) x < z b) ∀ y ( ( x-z ) y 2 6 = 1 ) 2) x ≤ z c) ∀ y ( ( x-z ) y 2 6 =-1 ) 3) x = z d) ∀ y ( x 6 = z-y 2 ) 4) x ≥ z e) ∀ y ( x 6 = z + y 2 ) 5) x > z 21-Sep-2010, 2:46 pm...
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