To provide a counterexample that proves the statement "If a number is divisible by 3, then it's odd" is false, we need to find a number that meets two criteria:
1. The number is divisible by 3.
2. The number is not odd (i.e., it is even).
Let's consider the number 6 as our potential counterexample.
1. Check if 6 is divisible by 3:
- A number is divisible by 3 if, when divided by 3, it results in an integer quotient with no remainder.
- Dividing 6 by 3 gives [tex]\( \frac{6}{3} = 2 \)[/tex].
- Since the quotient is an integer and there is no remainder, 6 is divisible by 3.
2. Check if 6 is odd:
- A number is odd if it is not divisible by 2; in other words, if divided by 2, it results in a non-integer quotient.
- Dividing 6 by 2 gives [tex]\( \frac{6}{2} = 3 \)[/tex].
- Since the quotient is an integer and there is no remainder, 6 is not odd; it is even.
Since the number 6 satisfies both criteria—it is divisible by 3 and it is even—it serves as a counterexample to the statement. This means that the original statement "If a number is divisible by 3, then it's odd" is false.
Thus, the counterexample is the number 6.
