Question

state the inverse, contrapositive, and converse of each conditional statement. then indicate whether the inverse, contrapositive, and converse are true. (a) if 3 is a prime number then 5 is an even number. (b) if 7 < 5, then 5 < 3.

Answer 1

The inverse is the false and the Converse is the true.

According to the statement

We have to find that the contra positive, and converse are true.

So, For this purpose, we know that the

A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences. For this conditional statement, P is called the hypothesis and Q is called the conclusion.

From the given information:

if 3 is a prime number then 5 is an even number.

Then

a) Inverse: If 3 is not a prime number, then 5 is not an even number. (True)

Contra positive: If five is not an even number, then 3 is not a prime number. (False)

Converse: If 5 is an even number, then 3 is a prime number. (True).

And

b) if 7 < 5, then 5 < 3

This statement is the false because the first statement is the false.

So, The inverse is the false and the Converse is the true.

Learn more about conditional statement here

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