47.7k views
2 votes
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

1 Answer

5 votes

Final answer:

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.

User Paval
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories