Question

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If a number is divisible by 4, then it is divisible by 6.

Short answer

The counterexample is number 16.

Step-by-step solution

Step 1. Define counterexample.

The counterexample is an example for which a hypothesis is true but the conclusion is false for an if-then statement.

Step 2. Observation of the statement.

In order to find a counterexample for the statement “If a number is divisible by 4, then it is divisible by 6.” we need to find a number that is divisible by 4 but not 6.

Step 3. State the counterexample.

Consider the number 16 which is divisible by 4. But clearly, 16 is not divisible by 6. Thus, the statement becomes false.

Therefore, the number 16 is a counterexample.