Ihe product of any evan integer and any odd intooer is cven. (a) Supese the given statement is rewriten in the lom, integes m and nc it Lhppothesis] ther Lcenclusian]. Fill in the blanks to deacribe the hyothes s and the canclusion. The conclusian is ! (b) The fulluwirg a s propesed prod of Ue given suedentent. 1. Suppoce mi Is any ovan latogor and a la ary cod Integor. 2. If mn Is even, then by defintion of eren there existe an inteper t guch that mi2r. 3. Alsu sirke m is even, there exisls an inleger p such thal w - 20 by definiliori of everi. 4. Ann since is odd, there exzite an integer q surh that n7q i 1 by terinition ot odd. 5. Thus, by subatiluliver, nn(20,(2q+1)2r, witete i is dil iriegel. 6. Hene, by derinition ot enso, then, mn is fuen, at wis to he shown. Reurber the sentences in the fulluwind scrambled list to explein the mistake in the propuesed provi. Step 5 deducas a canclusion that would be true if s were knewn to te trua. Ihe truth of S is not krown at the point where 'jtap 5 cccurs because the ageumpten that nn is eren has not been proved. Step 2 slotes thet the truth of S aould fulluw from the dssamplior thel. in n is evei. Hense, the proposed proof is clreular; it assumes what is to te proved. I hus, the conclusion in 'stes 2 is not a valid deduction. Let s be the seriberve. "There ts an inieget r such that m - a equals 2r.1 1. -iclst- 3. -5ela-t- 4. - Selact- 0. -ielact- 7. Selex