A number is in a only if it is in b A number is in b if it is in a C is a subset but not a proper subset of b A number is in b if and only if it is in c, and a number is in c if and only if it is in b. Yes, the person would yell once you fell, but only if you fell If and only if used in the same way means the same thing, except that only if is more forceful, more compelling
If and only if is the most obligatory of the three, in which the action has been distinguished and emphasised, if, and only if it's the most forceful of the three Read and learn about if and only if vs If or only if, what’s the difference On the alphascore lsat prep blog. It only states that an instance of a requires an instance of b, but it doesn't specifically say that an instance of b requires an instance of a That's why [a only if b] is sufficient to express the conditional statement [a → b].
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 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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