The correct answer here is C-> M because that is the option that ends up linking all of the conditional statements. P1: C-> Not E (Contrapositive E -> Not C) P2: D-> M (Contrapositive Not M -> Not D) P3: Not D -> E (Contrapositive Not E -> Not D).
We can connect the contrapositive of P2 with P3 to get Not M -> Not D -> E, and then add the contrapositive of P1 to get Not M -> Not D -> E -> Not C, and simplify this answer to Not M -> Not C. The contrapositive of this is C -> M, so therefore C->M is the correct answer. Remember that a contrapositive is a logically identical way to write a conditional statement, so we can think of it as just a different form of the same statement.
The reason Not C -> Not M doesn't work is because a) it would be an illegal negation of our correct answer (if we want to negate both sides of a conditional we need to also flip the conditions to turn it into a contrapositive) and b) we can't reach the statement Not C -> Not M just based on connecting our original premises. Hope this helps!
sia.aleem9@gmail.comMay 11, 2022
Hi there, I am unsure why for P3, the contrapositive of Not D -> E is Contrapositive Not E -> Not D. If we flip and negate the conditions, as in P1 and P2, wouldn't the correct contrapositive of P3 be Not E -> D?
Emil-KunkinMay 13, 2022
Hi,
Good catch- this looks like a typo from the rest of the paragraph, but thank you for pointing it out. The contrapositive of P3 should indeed be Not E - D
