original statement vs contrapositive statement

Hello, I apologise if this has already been discussed before. I am having difficulties with answering questions (on the flashcards) when it comes to identifying the missing premise because I continue to guess an answer that is the contrapositive of the original statement. For example: P:not X --> not Y P:? C: not x --> not B I had guessed the right answer was not Y-->not B, but the correct answer was B-->Y. How do I know that it was not asking for my answer? Don't they have the same meaning? Thank you!

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Ravi June 28, 2019

@tori06koto,

Great question. not Y - >not B and B - >Y are logically equivalent statements.

Since they mean the same thing, they are both two ways of stating the
correct answer choice.

Your guess was correct, and the stated answer of B - >Y is also right
since both statements mean the same thing.

It doesn't matter whether the answer is framed as the original
statement or the contrapositive because the statements are logically
the same.

It's like having an answer that says "2x2" instead of "4." "2x2" and
"4" mean the same thing, so both are correct.

Does that make sense? Let us know if you have any other questions!

tori06koto July 1, 2019

It makes perfect sense! thank you so much - your answer was very helpful!!

Ravi July 1, 2019

@tori06koto, you're welcome! Happy to help!