Disproof by counter-example Quiz

1. One counter-example to a statement shows that

• A. the statement is true
• B. the statement is false
• C. more tests are needed
• D. the statement is true except for that case

2. Which value of $n$ is a counter-example to '$n^2>n$ for every positive integer $n$'?

• A. $2$
• B. $3$
• C. $10$
• D. $1$

3. Which pair of primes is a counter-example to 'the sum of two primes is even'?

• A. $2$ and $3$
• B. $3$ and $5$
• C. $5$ and $7$
• D. $7$ and $11$

4. A student tests 10 cases and finds no counter-example. What can be concluded?

• A. The statement is true
• B. The statement is false
• C. Nothing is certain: a proof is needed
• D. The statement is true for all $n\ge10$

5. Which value is a counter-example to 'if $x^2>9$ then $x>3$'?

• A. $x=4$
• B. $x=5$
• C. $x=3.5$
• D. $x=-4$