Theorem: The product of every pair of even integers is even. Proof: 1. Suppose there are two even integers m an n whose sum is odd 2. m=2k1, for some integer k1 3. n=2k2, for some integer k2 4. m+n=2k1,+2k2 5. m+n=2(k1,+k2), where k1+k2 is an integer 6. m+n is even, which is contradiction Which of the following best describe the contradiction in the above proof by contradiction? Line 6 contains the entire contradiction Lines 1 and 2 contradict line 1 Line 4 contradicts line 1 Line 6 contradicts line 1 Question 2 Theorem: The sum of two even integers is even. Proof: Let m and n be any two arbitrary odd integers: 1. m=2k1, for some integer k1 2. n=2k2, for some integer k2 3. m+n=2k1+2k2 4. m+n=2(k1+k2), where k1+k2 is some integer 5. m+n is even In the proof shown above, what is the correct justification in the fourth step for the claim that k1+k2 is an integer? Definition of odd integers Algebra Definition of even integers Integers are closed under addition