Question

Which is the converse of the conditional statement and is it true or false?

If a number is a whole number, then it is a rational number.


If a number is not a whole number, then it is not a rational number. The converse is false.

If a number is a rational number, then it is a whole number. The converse is false.

If a number is not a rational number, then it is a whole number. The converse is false.

If a number is not a rational number, then it is not a whole number. The converse is true.

Answer 1

To form the converse of the conditional statement, interchange the hypothesis and the conclusion.

If a number is a whole number, then it is a rational number.

If a number is a whole number, is hypothesis and then it is a rational number is the conclusion.

So, its converse will be : If a number is a rational number, then it is a whole number. The converse is false.

The converse is true. Because every rational number can be written as a fraction p/q, where p and q are integers. So, if a number is a whole number, it must also be an integer and a rational. ALL whole numbers are rational numbers.

Answer 2

If a number is not a rational number, then it is not a whole number. The converse is true.
---> the sentence above is the only one that has true condition, true hypothesis and true conclusion.

You see:
>If a number is not a whole number, then it is not a rational number. The converse is false. ( converse must be true)
>If a number is a rational number, then it is a whole number. The converse is false. (converse must be true)
>If a number is not a rational number, then it is a whole number. The converse is false. (hypothesis should've been "then it is not a whole number")

In the Law of Detachment, if both conditional and hypothesis are true, then the conclusion is true.
All whole numbers are rational numbers.
In the "If-the"n form: If a number is whole, then it is rational.
Given: 5 is a whole number.
Conclusion: 5 is rational.