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shakenbake021 wrote:How do you diagram the following:

If it is not A, then B only if C.

Thanks!

r6_philly wrote:!A -> (B -> C) would be more accurate. the two condition is not parelle, first causes the second condition. IF not A, THEN B... because the reverse is: if A is true then the second condition is not necessarily true. You can't write it as a "and", it is causal.

itsfine wrote:

shakenbake021 wrote:How do you diagram the following:

If it is not A, then B only if C.

Thanks!

this is correct if it means : if it is not A, then it is B, so long as C.



(not a -> B ) -> c

tomwatts wrote:

r6_philly wrote:!A -> (B -> C) would be more accurate. the two condition is not parelle, first causes the second condition. IF not A, THEN B... because the reverse is: if A is true then the second condition is not necessarily true. You can't write it as a "and", it is causal.

You know, this is what I first wrote down, but then I changed my mind. I'm pretty sure that what I wrote performs identically to this (at least for LSAT purposes), but it's easier to write a contrapositive.

For instance, if we know we have not A, then we don't know whether we've got B or C. But if we know that we have not A and we know that we have B, then we know we have C. That comes out the same either way. On the other hand, if we know that we don't have C, then we know that we either don't have B or we have A (or both). That's pretty simple to get from the conditional that I wrote, but the contrapositive of yours would be...
!(B->C)->A
And frankly, I don't think I want to think about that on the LSAT.

This is just my second inclination, though, and my first inclination was what you wrote. Am I wrong in some way? Is there some reason that you have to write it the way that you did?