Disprove the following statement by giving a counterexample. For every integer n, if n is even then n2 + 1 is prime. Counterexample: Consider the ordered pair (n, n2 + 1) The values in the ordered pair show that the given statement is false because (choose one) n is even and n2 + 1 is prime. n is even and n2 + 1 is not prime. n is not even and n2 + 1 is prime. n is not even and n2 + 1 is not prime.

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Q: 10. Let a and b be natural numbers that are co-prime. Prove that (b-a) and b must also be co-prime.

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Q: 1. Is the following statement true? If yes prove. If no give a counter example. If a and b are any…

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A: Let us answer above questions

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A: We will use knowledge of number theory to answer this question.

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Q: 12. Consider the following (true) claim and two possible proofs. Claim. If n is a positive integer,…

A: Claim:   If n is a positive integer, then n2+3n+2 is not a prime number.