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.

Question

Mathematics

Makai Durham

1 March, 07:51

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.

+4

Answers (1)

Know the Answer?

Lucian Barr · Answer 1

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.