Consider the following statement The product of any even integer and any odd integer is even (a) Suppose the given statement is rewritten in the form, V integers m and n, if (hypothesis) then conclusion]. Fill in the blanks to describe the hypothesis and the conclusion Select The hypothesis is The conclusion is --Select- (b) The following is a proposed proof of the given statement 1. Suppose m is any even integer and n is any odd integer. 2. If min is even, then by definition of even there exists an integer r such that m. n = 2r. 3. Also since m is ever, there exists an integer p such that m = 2p by definition of even. 4. And since n is odd, there exists an integer a such that n.29 + 1 by definition of odd. 5. Thus, by substitution, m. n = (20)(20 + 1) = 2r, where ris an integer. 6. Hence, by definition of even, then, m.n is even, as was to be shown. Reorder the sentences in the following scrambled list to explain the mistake in the proposed proof Hence, the proposed proof is circular; it assumes what is to be proved. Step 2 states that the truth of S would follow from the assumption that min is even Thus, the conclusion in Steps is not a valid deduction, Step 5 deduces a conclusion that would be true ifs were known to be true. The truth of Sis not known at the point where Step Soccurs because the assumption that m. nis even has not been proved Since the truth of Step 6 depends on the truth of the conclusion in Step 5, Step 6 is not a valid deduction Let S be the sentence, "There is an integer r such that mn equals 2" Select appropriate sentences from the list and put them in the correct order to explain the mistake in the proposed proof. 1. Select --Select- --Select- Select Select 6. Select 7 Select NO