3 - Discrete Structures Semester 062 Major Examination I M...

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Discrete Structures Semester 062 Major Examination I Max Time allowed: 01:15 Hours Name: I.D. No.: Section I Total 1 20 I I 0 1 Question 1 2 Department of Information & Computer Science King Fahd University of Petroleum & Minerals Full Marks 7 4.5 Score

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(b) Define the Method of Indirect Proof. Problem 1- [0.6+0.4+1+1.5+1.5+2 points]: (a) Answer the followings as True (T) or False (F). Ans: Since the implication p 4 q is equivalent to its contrapositive, -q -+ -p, the implication p can be proved by showing that its contrapositive, -q + is true. An argument of this type is called an indirect proof. (c) Give an indirect proof of the theorem "If 3n + 2 is odd, then n is odd." Ans T T T No. (i) (ii) (iii) 4- Ans: Assume that the conclusion of this implication is false; namely, assume that n is even. Then n = 2k for some integer k. It follows that 3n + 2 = 3(2k) + 2 = 6k + 2 = 2(3k + I), so 3n + 2 is even (since it is a multiple of 2). Since the negation of the conclusion of the implication implies that the hypothesis is false, the original implications is true.
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3 - Discrete Structures Semester 062 Major Examination I M...

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