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In writing, phrases commonly used as alternatives to p if and only if q include (1) p only if q Q is necessary and sufficient for p, for p it is necessary and sufficient that q, p is equivalent (or materially equivalent) to q (compare with material implication), p precisely if q, p precisely (or exactly) when q, p exactly in case q, and p just in case q

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I'm understanding the basic idea of contraposition, when it comes to propositional logic and writing proofs, but i'm having trouble figuring out what the contraposition of p if and only if q woul. The following three statement patterns are logically equivalent 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. Learn the meaning and truth tables of implies and iff (if and only if) in mathematics See examples, definitions and tips to remember the difference between them.

The statement “p if and only if q” is a logical connective used in mathematics and logic, also known as “biconditional” or “equivalence” It means that p and q are both true or both false. 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.

Now, “a only if b” is true but “a if b” is false

So a only if b and a if b are not equivalent They must be saying something different They have a different logic. here is a summary of the different logical behavior of if as opposed to only if