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Prove that if n is an integer, these four statements are
Chapter 7, Problem 41E(choose chapter or problem)
QUESTION:
Prove that if n is an integer, these four statements are equivalent: (i) n is even, (ii) n + 1is odd, (iii) 3n + 1 is odd, (iv) 3n is even.
Questions & Answers
QUESTION:
Prove that if n is an integer, these four statements are equivalent: (i) n is even, (ii) n + 1is odd, (iii) 3n + 1 is odd, (iv) 3n is even.
ANSWER:SOLUTIONStep 1We need to prove that the given statements are equivalent.1. is even 2. is odd3. is odd4. We know that all the even numbers are of the form and all the odd numbers are of the form