5a * 3. Prove that if n is an odd integer, then n = 4k +1 for some integer k orn = 4k + 3 for some integer k.* 4. Prove the following proposition:For each integer a, if a2 = a, then a = 0 or a = 1.5.(a) Prove the following proposition:For all integers a, b, and d with d 0, if d divides a or d dividesb, then d divides the product ab.Hint: Notice that the hypothesis is a disjunction. So use two cases.(b) Write the contrapositive of the proposition in Exercise (5a).* (c) Write the converse of the proposition in Exercise (5a). Is the conversetrue or false? Justify your conclusion.6. Are the following propositions true or false? Justify all your conclusions. Ifa biconditional statement is found to be false, you should clearly determineif one of the conditional statements within it is true. In that case, you shouldstate an appropriate theorem for this conditional statement and prove it.* (a) For all integers m and n, m and n are consecutive integers if and onlyif 4 dividas (m2 1 1211

Name: 5a * 3. Prove that if n is an odd integer, then n = 4k +1 for some int
Uploaded: 2024-03-20T07:06:41.000Z
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Description: 5a * 3. Prove that if n is an odd integer, then n = 4k +1 for some integer k orn = 4k + 3 for some integer k.* 4. Prove the following proposition:For each integer a, if a2 = a, then a = 0 or a = 1.5.(a) Prove the following proposition:For all integer