# Week 4(15) Written Homework.pdf - MAT 243 Week 4/15...

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MAT 243 Week 4/15 Written Homework After you read the lecture and example pdf’s, read ”Avoiding Common Mis- takes in Proof Writing” page on Canvas which describes the mistakes that many 243 students make. In your proof, you can use ”obvious facts” and simple the- orems that we have proved previously in lecture. There are 8 problems in this homework set. Problem 8 is on the second page of the pdf. 1. (a) (2 points extra credit) When the conditional statement p q needs to be proved, state what needs to be assumed and what needs to be proved to justify the statement: using direct proof, using proof by contraposition, using proof by contradiction. (b) When a quantified statement ” x yP ( x, y ) is true” has to be proved using direct proof techniques, how would you proceed? Explain. 2. (3 points) Prove directly that the product of an even and an odd number is even. 3. (3 points) Prove by contraposition for arbitrary x 6 = - 2: if x is irrational, then so is x x +2 .