TTX wrote:Can someone show me how to take the contrapositive of the following conditional statement?
Original: If A but not B, then C.
It's from PT 62 (Dec. 2010), LR 1, Question 19.
I choose the wrong answer choice E, and I wonder why is it wrong for me to conclude that: if ~C, then either ~A or B.
The premise you're referencing is that any pet store that sells tropical fish but not exotic birds does sell gerbils.
TF + ~EB --> G
Answer choice (E) also uses the last premise that if the pet store is independently owned, it does not sell gerbils.
IO --> ~G
We can infer:
TF + ~EB --> ~IO
Answer choice (E) can be notated:
IO + ~TF --> EB
This is real close, but it should have stated:
IO + TF --> EB
According to the stimulus, if the store in not independently owned, then either it does not sell tropical fish or it does sell exotic birds. So if it sold tropical fish, we could infer that it sold exotic birds. Or if it did not sell exotic birds, we could infer that it did not sell tropical fish.