Solving Complex If/Then Statements

[qwpoi]

This is driving me nuts. I'm sure the answer is completely obvious.

I'm using > for the if A then B b/c there's no keyboard symbol for that, and * for the and operator because same reason.

1. B v (S*N)
2. B > ~S
3. S > ~ N / B v W

I have no idea what to do with these if/then statements, how to separate them, or anything, because I can't get any of the premises by themselves from the first statement.

Please help? Thanks.

 

[HallsofIvy]

I have no idea what your question is. Are these three statements the hypotheses and you want to decide what you can prove from them? Are they steps in a proof any you want to decide what you conclude? Is the last step the conclusion and you want to know if the argument is valid? What is it you want to know?

 

[qwpoi]

Sorry, should have explained more. It's a logical proof, and we have so far learned the a bunch of rules of inference and replacement. I had an epiphany in class though that I was forgetting one rule, and so was able to do it.

solution:
1. B v (S*N)
2. B > ~S
3. S > ~ N / B v W
4. (B>~S) * (S>~N) 2, 3 Conj
5. (BvS)*(BvN) 1 dist
6. BvS 5, simp
7. ~Sv~N 4, 6 CD
8. ~(S*N) DM 7
9. (S*N)vB 1 comm
10. B 8, 9 DS
11. BvW add 10