Prove that if n is positive integer, then n is odd if and only if 5n + | Discrete Structures 2078

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Discrete Structures20785 marksProof Methods

Prove that if n is positive integer, then n is odd if and only if 5n + 6 is odd. [5]

We must prove a biconditional statement: n is odd $\iff$ 5n + 6 is odd A biconditional proof requires proving both directions: 1. (Forward) If n is odd, then 5n + 6 is odd. 2. (Backward) If 5n + 6 is odd, then n is odd. We use the standard definitions: - An integer k is odd if there exists an int...

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We must prove a biconditional statement: n is odd $\iff$ 5n + 6 is odd A biconditional proof requires proving both directions: 1. (Forward) If n is odd, then 5n + 6 is odd. 2. (Backward) If 5n + 6 is odd, then n is odd. We use the standard definitions: - An integer k is odd if there exists an int...