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QUESTIONS Question 1. Is the following claim true or false? Justify your answer. Claim. For all integers a, if > 1 is even, then 4 | (a 1). Question 2. Determine whether the following claim is true or false. Prove your answer. Claim. For all integers n, if n is odd, then 8 | (n? 1). Question 3. Prove the following claim. Claim. There are no positive integers a and n such that n > 2 and a?+1=2" Question 4. Prove or disprove the following claim. Claim. Let a and b be real numbers. If b is irrational, then a + b is irrational or b is irrational. Question 5. Prove or disprove the following claim. Claim. For all real numbers r, if # = 2, then r is irrational