Question

Test the conditional statement and it’s converse to determine whether the following biconditional is true. A number is divisible by 6 if and only if it is divisible by 3.

Answer 1

Answer:

Given Statement is not bi-conditional.

Step-by-step explanation:

Given Statement: A number is divisible by 6 if and only if it is divisible by 3.

To check: It is bi conditional or not.

Forward Statement:

If a number is divisible by 6 then it also divisible by 3.

we know that if a number is divisible by 2nd number then it is divisible by all the factors of the 2nd number.

Factors of 6 = 1 , 2 , 3 , 6.

Here a number is divisible by 6 then it must be divisible by 1 , 2  and 3.

So, This statement is true.

Converse Statement:

If a number divisible by 3 then it also divisible by 6.

Here, lets take number = 27.

27 is divisible by 3 but it is not divisible by 6.

So, This statement is not true.

Therefore, Given Statement is not bi-conditional.

Answer 2

This is true. 6 has factors 1,2,3 and 6 so any number divisible by six is automatically divisible by all of its factors as well.