Which statement represents the inverse of the statement, "If it is snowing, then Paul wears a sweater"?
A. If Paul wears a sweater, then it is snowing.
B. If Paul does not wear a sweater, then it is not snowing.
C. If it is not snowing, then Paul does not wear a sweater.
D. If it is not snowing, then Paul wears a sweater.
is it B
No, B is the contrapositive.
(C) is the inverse
Take a look at
http://www.jimloy.com/logic/converse.htm
To find the inverse of a statement, you need to negate both the hypothesis and the conclusion. In this case, the statement "If it is snowing, then Paul wears a sweater" has the hypothesis "it is snowing" and the conclusion "Paul wears a sweater."
So, to find the inverse, we need to negate both parts of the statement. The negation of "it is snowing" is "it is not snowing," and the negation of "Paul wears a sweater" is "Paul does not wear a sweater."
Now we can look at the answer choices:
A. If Paul wears a sweater, then it is snowing. (Not the inverse)
B. If Paul does not wear a sweater, then it is not snowing. (This is the inverse)
C. If it is not snowing, then Paul does not wear a sweater. (Not the inverse)
D. If it is not snowing, then Paul wears a sweater. (Not the inverse)
So, you are correct! The correct answer is B, "If Paul does not wear a sweater, then it is not snowing."