MATH135 Study Guide - Midterm Guide: Contraposition, University Of Waterloo, Commutative Property

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: John Paul

Document Summary

002 (cid:3) 001, 010 (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) 011, 012 (cid:3) Marking scheme: fill in your name, id number, sec- tion, and sign the paper, answer all questions in the space provided. If you run out of space, continue on the back of the pre- ceding page, indicating where your work continues. The last page is for rough work: no calculators allowed, your grade will be in uenced by how clearly you express your ideas, and how well you organize your solu- tions. Page 2 of 10: let a, b and c be statements. Suppose we know that: (a = b) (( a) b) , and (a b) (( a) ( b)) and that (a b c) (a c b). Without using a truth table, but by using the logical equivalences discussed above, prove that. [(a b) = c] [(a c) = b] . [(a b) = c] [ (a b) c] defn of implication.