Proof by deduction and exhaustion Quiz

1. Which expression represents any odd integer?

• A. $2n$
• B. $2n+1$
• C. $2n^2$
• D. $n+2$

2. Proof by exhaustion is suitable when

• A. there are infinitely many cases
• B. the statement is false
• C. one example works
• D. there is a finite number of cases that can all be checked

3. Simplify $(2k+1)^2-1$.

• A. $4k(k+1)$
• B. $4k^2$
• C. $2k(k+1)$
• D. $4k^2+2k$

4. A student shows that $3+5=8$ and $7+9=16$ are even and concludes that the sum of two odd numbers is always even. This is

• A. a valid proof by exhaustion
• B. a proof by deduction
• C. not a proof, as it only checks examples
• D. a counter-example

5. Which algebra correctly starts a proof that the product of two even integers is a multiple of 4?

• A. $2n\times2n=4n^2$
• B. $2n\times(2n+1)$
• C. $2m\times2n=4mn$
• D. $2n+2n$