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My name is Dr. Lars Enden. I used to be a professor of philosophy and logic. I did that for about 20 years. But now, I am an LSAT tutor, and I have been doing this full-time for over 3 years.
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When you hear sufficient, you should think "enough," as in "I have had sufficient food for today." So, the sufficient condition is the one that is enough to ensure the truth of the other condition.
When you hear necessary, you should think "needed," as in "Food is necessary for my survival." [In other words, if you take away the food, I will not survive.] So, the necessary condition is the one that is needed for the other condition to be true.
Example: If it is raining, then the streets are wet.
"It is raining" is the sufficient condition because it is enough to bring about the wet streets. (Notice that the rain is not needed to bring about the wet streets because the streets can be wet for other reasons.)
"The streets are wet" is the necessary condition because it is needed for the rain. That might sound kind of weird, but if you think about it, taking away the wet streets would mean that we also have to take away the rain. So, the wet streets are in fact needed for the rain.
In general, the "if" part of a conditional is the sufficient condition, and the "then" part is the necessary condition.