Theorem: The sum of any even integer and any odd integer is odd. Construct a proof for the theorem by selecting sentences from the following scrambled list and putting them in the correct order. So by definition of even, t is even. By substitution and algebra, m + n = 2r + (2r + 1) = 2(2r) + 1. By substitution, m + n = 2t + 1. By definition of even and odd, there is an integer r such that m = 2r and n = 2r + 1. Let t = 2r. Then t is an integer because it is a product of integers. Let t = r + s. Then t is an integer because it is a sum of integers. Let m + n be any odd integer. Suppose m is any even integer and n is any odd integer. By definition of even and odd, there are integers r and s such that m = 2r and n = 2s + 1. By substitution and algebra, m + n = 2r + (2s + 1) = 2(r + s) + 1. Hence, m + n is two times an integer plus one. So by definition of odd, m + n is odd. Proof: 1. Suppose m is any even integer and n is any odd integer. 2. By definition of even and odd, there are integers r and s such that m = 2r and n = 2s +1. 3. So by definition of even, t is even. 4. Let t = 2r. Then t is an integer because it is a product of integers. 5. Let m + n be any odd integer. 6. By substitution and algebra, m + n = 2r + (2s + 1) = 2(r + s) + 1. X

In a traditional class with in-class tests, a question that is often asked after a class exam is, "What was the class average?" If that question is asked and the professor says that the class average was 80, what information do the students gain by knowing that? I want you to focus on both what the individual students knows about their own grade as well as what the students know about the class's grades on that exam.

In 2004 it surfaced in Reader's Digest presented as having happened to a teacher at an unnamed community college. Four students walked in halfway through American history test my father was giving at the local community college. "Sorry," they said, "we had a flat tire." An understanding man, Dad said that if they could answer just one question correctly, he would give them each an "A" for the exam. The students agreed. So my father handed each one a piece of paper, placed them in four separate comers and said, "Write down which tire was flat." Kurt Smith What is the probability that these four students would give identical answers if they hadn't had a flat tire? Why?

I already have a,b,c and d. I just need help on E, F, G, and H