A conditional is a sentence expressing a hypothetical relationship, as when we say “If Alice studies she will pass” or “Alice will pass only if she studies.” We are not making the claim that Alice will pass no matter what, but we are making her passing depend on something else (study) as either a sufficient condition or a necessary condition.

The standard form of a conditional statement is “If P then Q”--symbolized as PQC. This is logically equivalent to the statement “P only if Q” as well as to “Not-P unless Q.”

A key thing to remember is that the word order in English does not itself determine the relationship. “If Alice studies she passes” expresses the same relationship (study as a sufficient condition) as “Alice passes if she studies,” but both are different from “Alice passes only if she studies” (study as a necessary condition).

We can also have joint conditions, as in “Alice will pass if she takes good notes and studies” or “Alice will pass only if she either has a good memory or has studied hard.” In a string such as PQARC we see PQA as a joint sufficient condition. In PQROC we see QRO as a joint necessary condition.

For additional practice, run the program STDFORM supplied on your disk.

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