Test the conditional statement and its converse to determine whether the following biconditional is true. A number is divisible by 6 if and only if it is divisible by 3. It is false because at least one part of the biconditional is false. It is false because both parts of the biconditional are false. It is true because at least one part of the biconditional is true. It is true because both parts of the biconditional are true.

Answer 1

The conditional statement in this case is "if a number is divisible by 6, then it is divisible by 3" and its converse is "if a number is divisible by 3, then it is divisible by 6."

To test the biconditional, we need to verify if both the conditional statement and its converse are true.

1) If a number is divisible by 6, then it is divisible by 3.
This statement is true. If a number is divisible by 6, it means it can be divided evenly by both 2 and 3. So, it is divisible by 3.

2) If a number is divisible by 3, then it is divisible by 6.
This statement is also true. If a number is divisible by 3, it means it can be divided evenly by 3. It can also be divided evenly by 2 because any number divisible by 3 is also divisible by 2.

Since both the conditional statement and its converse are true, the biconditional statement "A number is divisible by 6 if and only if it is divisible by 3" is true. Hence, the correct answer is: It is true because both parts of the biconditional are true.