2. Proof Techniques I

Direct Proof — Quiz

Test your understanding of direct proof with 5 practice questions.

Practice Questions

Question 1

In mathematics, what is a direct proof?

Question 2

To begin a direct proof of the statement "If $n$ is even, then $n^2$ is even," which assumption should be made?

Question 3

If $a=2m$ and $b=2n$ for integers $m$ and $n$, what is a correct expression for $a+b$?

Question 4

If $m=2r+1$ and $n=2s+1$ are odd integers, what is $m+n$ equal to?

Question 5

To prove directly that every multiple of $10$ is even, how can $x$ be written?