Answer :
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.
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.
