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.
(a) (2 points extra credit) When the conditional statement
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 ”
) 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
3. (3 points) Prove by contraposition for arbitrary
then so is