I just begin learning propositional logic and find a little bit confused when trying to translate the contrapositive of an implication back to the English language.
For example, I have an implication: p implies q.
p: it is raining. q: the home team wins.
Therefore, this implication means: if it is raining, the home team wins. "it is not raining, the home team wins" is also right since this is not an "only if" case, the home team can also win when they hear cheers. However, "if it is raining, the home team loses" is false since "raining" will be a sufficient condition for q to occur.
I think my reasoning above is correct. And here is my confusion. As I know that contrapositive of an implication is equivalent to the implication, so I try to translate this contrapositive back to the English language to see whether it works:
The contrapositive of "it is not raining, the home team wins", from my perspective, should be:
"If the home team loses, it is raining". And this true contrapositive seems to be similar to that false statement "if it is raining, the home team loses", as I think that raining and losing cannot happen together. Thus this contradiction puzzles me a lot. Could anyone help me? Is there any weakness or error in my reasoning? Thanks in advance.