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In writing, phrases commonly used as alternatives to p if and only if q include That p is true and q is false. 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

7 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 would be. That is, p only if q rules out just one possibility 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. 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.

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. 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.

P only if q means that the truth of q is necessary, or required, in order for p to be true

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