Daily Drills 31 - Section 31 - Question 3

P: not X → YP: X → not ZP: not Z → WC: ?

Alex-Hoston June 8, 2022

Contrapositives

Based on how the explanation of the answer was given I’m confused. To solve the conclusion it says to take the contrapositive of the 1st premise Y>>X And then added it to the 3rd premise NotZ>>W So I guess my question is, when is it ok to use the premise that is given vs when can we use the contrapositive of that premise and still get the correct answer?

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Emil-Kunkin June 10, 2022

Hi Alex,

We can always use the contrapositives, and we can always use the original statements. While these drills are meant to show us the pure logic, on real questions the correct answer must be something that we can show answers the given question. For a must be true question (which is the most diagram-heavy question type), the correct answer could be found by only using the original statements, only using contrapositives, or putting together an original statement and a contrapositive (or more than one). Ultimately, a contrapositive is just a restatement of the original statement. They are logically equivalent.

Alex-Hoston June 22, 2022

Got it ok thank you