Proof by contradiction Quiz

1. To prove by contradiction that there is no greatest even integer, what do you assume?

• A. Every integer is even
• B. There is no greatest even integer
• C. There is a greatest even integer
• D. There is a greatest odd integer

2. In the proof that $\sqrt2$ is irrational, $p^2=2q^2$ shows $p$ is even. What is the next step?

• A. Write $p=2k$ and substitute
• B. Write $p=2k+1$ and substitute
• C. State that $q$ is odd
• D. State that $p$ is prime

3. For the list $2,3,5,7$, Euclid's number is $N=211$. Which statement is correct?

• A. $N$ is divisible by 3
• B. $N$ is divisible by 7
• C. $N$ is even
• D. $N$ is prime and is not in the list

4. In proving there are no integers with $14m+21n=1$, which statement gives the contradiction?

• A. $14m+21n$ is always even
• B. The left-hand side is a multiple of 7 but 1 is not
• C. $m$ and $n$ must both be zero
• D. $14m+21n$ is always odd

5. What is the negation of 'for all integers $n$, $n^2$ is even'?

• A. For all integers $n$, $n^2$ is odd
• B. There is no integer $n$ with $n^2$ even
• C. There exists an integer $n$ with $n^2$ odd
• D. There exists an integer $n$ with $n^2$ even