Chapter 1 - Section 1.7 - Introduction to Proofs - Exercises - Page 91: 6

See proof.

Suppose we have 2 odd integers, $2n+1$ and $2m+1$ where $n,m$ are integers. Multiplying our odd integers we get $(2n+1)(2m+1)=4mn+2m+2n+1=2(2mn+m+n)+1$. Since $n$ and $m$ are integers $2mn+m+n$ must be as well so we have 2 times an integer plus 1 which must be an odd number. Thus, the product of 2 odd integers is also odd.