Identify what you can properly conclude from the given premises:
P: not A → B P: A → not Z P: not Z → F C: ?
josh0327November 5, 2020
Bad assumption
The initial premise, if not A then B, does not allow you, on its own, to assume that if not B then A.
The truth and falsity conditions for the material conditionals that seem to be used there don’t make that follow by necessity.
What you can say, is that if a thing is not an A, then it is a B.
That still leaves open the possibility of a thing being both an A and a B.
Which would then make none of the answers provided correct if you’re looking for something that follows by necessity.
What am I missing?
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"The initial premise, if not A then B, does not allow you to, on its own, assume that if not B then A."
Actually, we can make that assumption! What you just described is a contrapositive. not A ---> B not B ---> A
A contrapositive carries the exact same logic as its counterpart. They are interchangeable. This drill is asking us to connect pieces of information to draw a conclusion. The best way to do that is to substitute the first premise for its contrapositive.
P: not B ---> A P: A ---> not Z P: not Z ---> F
Putting them together: not B ---> A ---> not Z ---> F
This allows us to conclude: not B --->F
B is the correct answer.
Keerthana January 14, 2021
But how do we know that it's a contrapositive? How are we able to assume that not B ---> A?
ybentJanuary 25, 2023
How do you know when to answer a question in contrapositive?
Emil-KunkinJanuary 26, 2023
Hi, a correct answer could either be it's statement or it's contrapositive. They are the same thing, it's like the difference between 1/2 or 50 percent.
MariyamJune 19, 2024
This statement REALLY helps:
"They are the same thing, it's like the difference between 1/2 or 50 percent."
