Q35. - Algebra 1

Question

Find a counterexample for each conditional statement.

If a number is divisible by 3, then the number is odd.

Step-by-Step Solution

Answer

"If a number is divisible by 3, then the number is odd" is false, and the counterexample is 12.

Step 1. Given Statement.

If a number is divisible by 3, then the number is odd.

Step 2. Description of step.

To find a counterexample for the given statement. 

Note that 3 is an odd number and it divides many odd numbers like 9, 15, 21, etc.

So we can say that some odd numbers that are divisible by 3.

But there are numbers like 12, 18, 24 which are even numbers yet divisible by 3.

Step 3. Conclusion.

Hence the statement that " if a number is divisible by 3, then the number is odd is false", and the counter example is 12.