Test the conditional statement and its converse to determine whether the following biconditional is true. A number is divisible by 10 if and only if it is divisible by 5. It is false because both parts of the biconditional are false. It is true because both parts of the biconditional are true. It is false because at least one part of the biconditional is false. It is true because at least one part of the biconditional is true

Question

Test the conditional statement and its converse to determine whether the following biconditional is true. A number is divisible by 10 if and only if it is divisible by 5. It is false because both parts of the biconditional are false. It is true because both parts of the biconditional are true. It is false because at least one part of the biconditional is false. It is true because at least one part of the biconditional is true

Answer 1

The correct answer is: It is true because both parts of the biconditional are true.

Answer 2

To determine whether the biconditional statement is true or false, we can test the conditional statement and its converse.

The conditional statement of the biconditional is "If a number is divisible by 10, then it is divisible by 5." Let's test this statement.

If we take the number 20, we can see that it is divisible by 10 since 20 ÷ 10 = 2 with no remainder. However, 20 is not divisible by 5 because 20 ÷ 5 = 4 with no remainder. Therefore, the conditional statement "If a number is divisible by 10, then it is divisible by 5" is false.

Now let's test the converse of the conditional statement. The converse is "If a number is divisible by 5, then it is divisible by 10." If we take the number 5, we see that it is divisible by 5 since 5 ÷ 5 = 1 with no remainder. However, 5 is not divisible by 10 because 5 ÷ 10 = 0 with a remainder of 5. Therefore, the converse of the conditional statement is also false.

Since the conditional statement and its converse are both false, we can conclude that the biconditional statement, "A number is divisible by 10 if and only if it is divisible by 5," is false.

Answer 3

To test the biconditional statement "A number is divisible by 10 if and only if it is divisible by 5," we need to examine both the conditional statement and its converse.

1. Conditional Statement: "If a number is divisible by 10, then it is divisible by 5."
- This statement is true because any number that is divisible by 10 (e.g., 10, 20, 30) is also divisible by 5.

2. Converse Statement: "If a number is divisible by 5, then it is divisible by 10."
- This statement is false because not all numbers divisible by 5 (e.g., 5, 15, 25) are divisible by 10.

Since the biconditional is only true when both the conditional statement and its converse are true, and in this case, the converse is false, the biconditional statement is false.