I see a lot of practice problems on these conditions to place statements in necessary, sufficient, both, or neither. What dictates a statement as both necessary and sufficient, and what makes a statement neither? I guess I understand the difference and correct me if I’m wrong:
Necessary: Impossible to have Y without X; Absence of X guarantees the absence of Y.
Sufficient: If X, then Y. X’s presence can cause Y, but it doesn’t have to.
What makes a statement both or neither? What makes something necessary but not sufficient? Is that like taking the LSAT to get into law school; it’s necessary, but it won’t guarantee your acceptance. Can you have a statement that’s sufficient and not necessary?
In: Other
Think about this example. If you had a fever, it would be sufficient to diagnose you with an illness, but it’s not necessary – you can have no fever and still be ill.
Yes what you said is right. It’s all about logical implications, and your last example was right.
Some examples that might help you understand more:
##Sufficient
If you insult your boss, you get fired.
It’s sufficient because that’s enough to get you fired, but it’s not necessary: you can be fired for other reasons, without ever having insulted your boss.
Something mathematical: multiplying two negative numbers gives you a positive number.
It’s sufficient to have two negative numbers to get a positive result, but it’s not necessary because you can get the positive result anyways by multiplying two positive numbers.
With sufficient conditions, the presence of those conditions imply the result. Multiplying two negative numbers implies a positive result.
##Necessary
You have to pass the admission test to get into that college.
It’s necessary, it can’t be otherwise. If you are in college, it means that you passed the admission test, there’s no other way.
But it’s not sufficient: you can pass the test, but get a low grade and not get your place.
Or, a more mathematical one: having four sides is a necessary condition to have a square, but it’s not sufficient. There are things that have four sides which are not squares, like rectangles.
With necessary conditions the result always implies the conditions: if it’s a square, then it has four sides. But the opposite is false.
##Sufficient and necessary
If you commit crime, you are a criminal.
Very intuitive: committing a crime is enough to make you a criminal, and it’s also necessary – you can’t be a criminal with no crimes.
Notice how in this case the relation is also reversible: if you are a criminal then you committed crime.
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