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Unformatted text preview: . .+2n=n(n+1) (a) What are i. (2 points) p(1): ii. (2 points) p(2): iii. (2 points) p(n+1): (b) (10 points) Prove p(n) ∀ n by mathematical induction. 8. (10 points) p ( n ) : n 2 + 5 n + 1 is odd Prove p(n) ∀ n ≥ 1 by mathematical induction. 2 9. Following relation R is represented by a directed graph (digraph). A B C D (a) (5 points) Write the relation R as a set of elements of R × R . (b) (12 points) Circle the appropriate properties below for the relation. refexive irrefexive symmetric antisymmetric asymmetric transitive (c) Find the powers R 2 , R 3 (5 points) R 2 = (5 points) R 3 = 10. Following relation is de±ned on the set A = { 1 , 2 , 3 , 4 } R = { ( a, b ) ²A × A  a ≡ b (mod 2) } (a) (5 points) Give the relation R as a set. (b) (1 points) Is it an equivalence relation? 3...
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 Spring '08
 SaktiPramanik
 Computer Science, Natural number, Prime number

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