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A is a proper subset of b To explore its intricacies, suppose that to get an a grade in math 101 you need to do two things A number is in a only if it is in b
A number is in b if it is in a The word only is an important one for logical purposes 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.
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]. Read and learn about if and only if vs If or only if, what's the difference
On the alphascore lsat prep blog. If only and only if are similar expressions that are used in different ways 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 The phrase if and only if is used in mathematics, logic, and statistical formulas Knowing how to use the phrase is essential for math mastery.
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.
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. Iff if and only if biconditional a way of writing two conditionals at once
Both a conditional and its converse For example, the statement a triangle is equilateral iff its angles all measure 60° means both if a triangle is equilateral then its angles all measure 60° and if all the angles of a triangle measure 60° then the triangle is equilateral Biconditionals can be written using. A phrase like p if and only if q appears to be an abbreviated way of saying p if q and p only if q
Once we notice this, we do not have to try to discern the meaning of if and only if using our expert understanding of english.
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