If A -> B and ~A -> C, what does ~C imply?

Question

If A -> B and ~A -> C, what does ~C imply?


1. ~A
2. B
3. ~B
4. It implies a contradiction


Answers on a postcard please.
(or just here will do thanks)

Answer 1

Since, ~A => C, the contrapositive is true:
~C => A.
And A=> B.
Therefore, ~C=> B.

Answer 2

B
If that arrow means equals then it means B and C are the same thing. If they are place names then it means A is a cross roads to B or C. If the arrows imply a one way system it means you can't reach A from B or C and that anything which reaches B or C has passed through A. Assuming these are all the facts and you are leaving the other letters of the alphabet out of it.
Not sure what to make of the ~. If it's something like 'absence of', you could say the absence of C implies the presence of A, which then implies B ( A not being an option). On the other hand, absence of C does not necessary imply presence of A (your q. gives the opposite), so a contradiction? it implies zip..

Answer 3

It implies a contradiction. As the previous answerers show, ~C would equal two different variables, which leads to a contradiction without more information.

Answer 4

Are you in symbolic logic? Your first line of logic is: ~C -> B

Answer 5

It doesn't imply any of those things; it implies A & B & ~C. Do the truth table of

(A > B) & (~A > C) & (~C);

that's what you will get.

Answer 6

2. B
~A -> C is equivalent to ~C -> A. Combining this with A->B gives you ~C ->B.

Answer 7

~C means A, and A means B. Therefore, ~C means B.

Answer 8

~A->C <-> ~C->A <-> A->B
thus 2)

Answer 9

what does wavy c mean