9. (4 points) Universal instantiation is used when we conclude that from the statement All women are wise," where Lisa is in the domain of all women 10. (5 points) Use a proof by contraposition, the definitions of even and odd integers, and the fact that any integer is either even or odd, to prove the following result, using complete, grammatical English sentences: If x is an even integer, then x +4 is an even integer. 11. (5 points) Prove using mathematical induction that the sum of the first n positive integers is n(n+1)/2. 12. (5 points) Use complete, grammatical sentences to explain clearly in idiomatic English why VxP(C) = 3x-P(x). 9. (4 points) Universal instantiation is used when we conclude that from the statement All women are wise," where Lisa is in the domain of all women 10. (5 points) Use a proof by contraposition, the definitions of even and odd integers, and the fact that any integer is either even or odd, to prove the following result, using complete, grammatical English sentences: If x is an even integer, then x +4 is an even integer. 11. (5 points) Prove using mathematical induction that the sum of the first n positive integers is n(n+1)/2. 12. (5 points) Use complete, grammatical sentences to explain clearly in idiomatic English why VxP(C) = 3x-P(x)