Use the proof type strong mathematical induction to prove that every positive integer greater than one is divisible by at least one prime number. That is, prove that the following formal statement is true, Vn e Z+, n > 1, Ep e Z+, p prime | (p | n) Half the points for this problem will be granted only if you show the correct form of the proof type. That is, showing formal start and end statements, explicitly proving any needed basis case, explicitly proving the strong mathematical induction step, and explicitly asserting that the requirements for strong mathematical induction have been met before you conclude the proof. You can use the Canvas math editor or English language sentences. You must use the 2-column statement/justification format for your proof. Every statement must be justified.

Write the contrapositive of the conditional statement. determine whether the contrapositive is true or false. if it is false, find a counterexample. a converse statement is formed by exchanging the hypothesis and conclusion of the conditional. a) a non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. true b) a statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. false; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional. c) a non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. false; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional. d) a statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. true