"Only attritbuted to" type questions and contrapositives

[hyk1310]

There are some questions that say, A can only be attributed to B.
For example, a sentence might be constructed like the following: being good at sports can only be attributed to one's genes.
Logically thinking, would this be the equivalent to A only if B (If you are good at sports, then it is due to your genes)? The "attributed to" aspect confuses me.

Furthermore, if we say that being good at sports can only be attributed to one's genes, would that mean that there are no other necessary conditions that are needed to satisfy the sufficient condition?


My second question is:

Say
#1 B--> C, B-->A.

And say that
#2 B--> C+A.

The contrapositives of the #1 and #2 seem to be the same, yet in their original forms, they seem to imply different things.

If C's domain of logic is not the same as A's domain, then the first statement seems to include realms/aspect that are not included by C+A (This would be easily visualized in a venn diagram).

How do we go about reconciling this?

Thank you!

[ohthatpatrick]

I'm afraid I don't know what you're referring to for the most part.

I've been doing LSAT for a decade, and it's not ringing much of a bell that we regularly see "X can only be attributed to Y".

If we DO see it, it would be diagrammed/thought of as you suggested:
X --> Y

But it's messier than that. Consider: "His refusal to go on a 2nd date with her can only be attributed to her looks".

How would I represent that?
"If he refuses to go on a 2nd date, then ..... "

I would have to say something like, "then ... it has SOMETHING to do with her looks".

But I wouldn't know from that claim whether the problem was that she was too pretty, not pretty enough, reminder him of his mother, etc.

So if I were to see "X can only be attributed to Y", it's unlikely that I would really think about it conditionally. I would just think causally, and I would know that LOOKS (something about them) were the only causal factor leading to his refusal of a 2nd date.

As far as your #1 vs. #2
B -> A
B -> C
vs.
B -> A and C

Those are identical in conditional logic (or at least in LSAT's domain of conditional logic).

The contrapositive to #2
~C or ~A --> ~B
can be split up to say
~C --> ~B
~A --> ~B
which is what you'd get from contraposing #1