How does B-Z become Not Z-Not B it was my logic that the contrapositive would simply be Z-B. If I am not initially given not Then how can I logically determine that if it's not z- not b.
Because if I were to complete the logical order based on what I was given that would be z-b
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This is one of the rules of inference, known as transposition or commonly referred to as contrapositive. A -> B is logically equivalent to ~B -> ~A
To illustrate why this is the case, let's consider the following statement:
Houses (A) have windows (B) that can be diagrammed as:
A -> B
Could we infer from this statement that everything that has a window is a house (B ->A)?
No, this would be a logical fallacy because if something has a window, it could be a car, an office building, a greenhouse etc. The only proper inference we can make is that if something does not have a window it is not a house because all houses must have windows.
~ B -> ~A
The more you practice, the more comfortable you should get with applying the rules of inference, but if it is not initially intuitive why these statements are logically equivalent, it might be helpful to memorize the rule.
Let me know if you have any further questions.
LamontDecember 31, 2021
I felt the logical flow started with P1 X-A P2 A-B and P3 B-Z =X-Z, then the contrapositive.
jakennedyJanuary 17, 2022
@Lamont,
That's exactly correct, but the answer can always take the contrapositive form. In this case, if you have:
