Question

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

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

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

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

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

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

Answer 1

A conditional is of the form:
If (hypothesis), then (conclusion).
To get the converse, just switch the hypothesis and the conclusion.

Answer 2

Can you figure out what the converse is?

Answer 3

Im pretty sure its d

Answer 4

The answer is not D.

To get the converse, you do not negate the hypothesis or the conclusion. You just switch them.

Once again:
To find the converse, just switch the hypothesis and the conclusion.

This is the given conditional:
\(If \color{red}{~a ~number ~is ~a ~whole ~number}, ~then \color{green}{~it ~is ~a ~rational ~number}.\)

The hypothesis is in red, and the conclusion is in green.
The converse is obtained by switching the hypothesis and the conclusion.
This is the correct converse of the given conditional:

\(If~\color{green}{~a ~number ~is ~a ~rational ~number} , ~then \color{red}{~it ~is ~a ~whole ~number}.\)

In this case we need to adjust the language a little to make it make sense, but the important thing is that the hypothesis and the conclusion switched positions.

The question now is "is the converse true or false?". The converse is false, so the correct answer is B.