Math Problem Statement

Consider this statement.

If a number is divisible by 3, then it's odd.

Provide a counterexample that proves the statement is false. Explain your reasoning.

Type the correct answer in the box.

Solution

The statement "If a number is divisible by 3, then it's odd" is false. A counterexample that proves this statement is false is the number 6.

Reasoning:

  • The number 6 is divisible by 3 (since 6 ÷ 3 = 2).
  • However, 6 is not odd; it is an even number.

Thus, 6 is a counterexample that disproves the statement.

Do you want more details or have any questions?

Here are five related questions to consider:

  1. What is the definition of an odd number?
  2. How can we determine if a number is divisible by 3?
  3. Can you find another even number divisible by 3?
  4. What is the difference between an odd number and an even number?
  5. How would you rewrite the original statement to make it true?

Tip: When asked to disprove a statement, finding just one counterexample is enough.