Hw2Sol.pdf - CMSC 203 Section 0201 Hw2 Solution 1 Exercise set 2.1 Problem 18 c,d Solution(10 points c ∀s ∈ C(s C(s → ¬E(s d ∃s ∈ C(s C(s �

Hw2Sol.pdf - CMSC 203 Section 0201 Hw2 Solution 1 Exercise...

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CMSC 203 : Section 0201 Hw2 Solution February 24, 2007 1. Exercise set 2.1 Problem 18 c,d (10 points) Solution c. s C ( s ), C ( s ) → ¬ E ( s ) d. s C ( s ), C ( s ) M ( s ) 2. Exercise set 2.2 Problem 3 b,d (10 points) Solution b. computer c , c has no CPU d. bands b , b has won less than 10 grammy awards Problem 12 (10 points) Solution Statement: The product of any irrational number and any rational number is is irra- tional Proposed negation: The product of any irrational number and any rational number is rational The proposed negation is incorrect. The correct negation would be: There exists at least one irrational and a rational number such that the product of those numbers is not irrational (rational) Problem 15 (10 points) Solution Given that D = { -48,-14,-8,0,1,3,16,23,26,32,36 } a. x D , if x is odd then x > 0 This is true b. x D , if x < 0 then x is even 1
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This is true c. x D , if x is even then x 0 This is false. Consider x = 16, 26, 32, 36 for these x the statement fails d. x D , if the ones digit of x is 2, then tens digit is 3 or 4 This is true e. x D
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