assignment-02

assignment-02 - R(a ∀ x ∃ y y 3 x = 0(b ∀ x ∃ y...

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MATH 135, Fall 2010 Assignment #2 Due at 4:00pm on Tuesday, September 28 For the online MapleTA assignment, please go to http://mapleta.uwaterloo.ca/ . Problem 1 . Let S = {- 5 , - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 , 5 } . List all of the elements in each of the following sets. (a) A = ± x S ² ² x is even and x is a multiple of 3 ³ . (b) B = ± x S ² ² if x is odd, then x is a multiple of 5 ³ . (c) A B . (d) A B . Problem 2 . For each of the following statements, determine whether it is true when the universe of discourse is Z and whether it is true when the universe of discourse is
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Unformatted text preview: R . (a) ∀ x ∃ y ( y 3 + x = 0) (b) ∀ x ∃ y ( y < x AND ∀ z ( z < x = ⇒ z ≤ y ) ) Problem 3 . (a) Let x,y ∈ Z . Prove that if x > 0 and x + y < xy , then y > (b) Let x,y ∈ R . Determine the following statement is true or false. Justify your answer. If x > 0 and x + y < xy , then y > 0. Problem 4 . Negate the expression ∃ x ∀ y, ( P ( x ) AND Q ( y ) ) and simplify your answer. 1...
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