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However, this usage of if and only if is relatively uncommon and overlooks the linguistic fact that the if of a definition is interpreted as meaning if and only if. To explore its intricacies, suppose that to get an a grade in math 101 you need to do two things Variations of only now that you can see how only if can be understood, let's cover a few variations of only that you're likely to encounter on the lsat:
Bonobos are the only primates, including humans, that don't kill others
If only and only if are similar expressions that are used in different ways The word only is an important one for logical purposes If only expresses a hope or wish
If only i had a real choice in the matter
She needed to get away from her job if only for a week == only if expresses a command or requirement He can stay on the team only if he completes his homework and improves his grades Only if what's the difference
If only and only if are both phrases that express conditions or possibilities, but they are used in slightly different contexts If only is often used to express regret or longing for a different outcome, while only if is used to set a condition or requirement for something to happen Both phrases can convey a sense of limitation or restriction. Only if is a conjunction which stipulates that what follows is necessarily and true
Its meanings include providing that, assuming that, and as long as
Sentences with if and sentences with only if can essentially mean the same thing, but only if is a stronger phrase That is, the conditional aspect of the meaning is more emphasized and prominent. This is why logicians use iff for 'if and only if' I think it would be useful in real life, but can't see it catching on.
In fact, when p if and only q is true, p can subsitute for q and q can subsitute for p in other compound sentences without changing the truth P if and only if q is rarely found in ordinary english The truth table below formalizes this understanding of if and only if T stands for true, and f stands for.
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