Question

What is the inverse of the following statement?

If it is raining, then I will carry an umbrella?

-If I carry an umbrella, then it is raining.
-If I do not carry an umbrella, then it is not raining.
-If it is not raining, then I will not carry an umbrella.
-I will carry an umbrella if and only if it is raining.

I don't understand this question. I just want someone to explain it. thanks :)

Answer 1

I believe it is the second one.

Answer 2

If it is not raining, then I will not carry an umbrella

Explanation:

we have

"If it is raining, then I will carry an umbrella" ----> This is a conditional statement

we know that

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion

so

If it is raining------> If it is not raining

I will carry an umbrella-------> I will not carry an umbrella

therefore

The inverse is

If it is not raining, then I will not carry an umbrella