Question

What is a counter example of the statement: 'If a number is divisible by three, then it is odd'?

1) 6
2) 9
3) 12
4) 15

Answer 1

The counterexamples to the statement 'If a number is divisible by three, then it is odd' are the numbers 6 and 12 since they are both divisible by three and are even, disproving the statement.

Step-by-step explanation:

The statement 'If a number is divisible by three, then it is odd' can be proven false with a counterexample. A counterexample is a specific case that shows the statement is not always true. In this instance, we are looking for a number that is both divisible by three and even.

Examining the provided options:

1. 6 is divisible by three and is even.
2. 9 is divisible by three but it is odd.
3. 12 is divisible by three and is even.
4. 15 is divisible by three but it is odd.

Both options 1) 6 and 3) 12 serve as counterexamples because they are divisible by three and are even numbers, which contradicts the statement. Therefore, we can use either 6 or 12 as a counterexample to show that the statement is incorrect.