57 LR Two Question 12
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Comments

If answer choice B is false then doesn't the argument fall apart? So why isn't B correct?

(B) isn't necessary.
Consider this example:
In order to be a successful team in the NBA, you have to be able to jump. No one on the Sixers has strong legs. That's why they're terrible at basketball.
To make this argument work, we must assume that strong legs are needed for jumping ability. If you were to say "But you don't need strong legs to jump!" then the argument would fall apart (which is why (E) is correct!).
However, you don't need to know that strong legs are sufficient to make you good. Let the Sixers jump to the moon; they'll still suck. That's why (B) is wrong; we don't need to know that strong legs (or international police) are sufficient.

I thought that E was a sufficient condition for the argument, not a necessary one

(E) is sufficient! It's also necessary (see above)—this is an example of an argument in which there's only one piece missing. That single bit, then, is both necessary to and sufficient for proof of the conclusion.