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# Propositions - if vs only if

In Propositions statements of “$$p$$ if $$q$$” and “$$p$$ only if $$q$$” have an inverse implication.

A proposition in the form $$p$$ if $$q$$ has the standard form “if $$q$$ then $$p$$”, or $$q \rightarrow p$$.

Statements of $$p$$ only if $$q$$ are equivalent to the standard form “if $$p$$ then $$q$$”, or $$p \rightarrow q$$.