(adsbygoogle = window.adsbygoogle || []).push({}); Difference between "only if" and "if and only if"

$$1.\quad p\quad if\quad q\\ \equiv if\quad q\quad then\quad p\\ \equiv q\rightarrow p\\ \\$$$$2.\quad p\quad only\quad if\quad q\\ \equiv if\quad p\quad then\quad q\\ \equiv p\rightarrow q\\ \\$$$$3.\quad p\quad only\quad if\quad q\\ \equiv if\quad q\quad then\quad p\\ \equiv q\rightarrow p\\ \\$$$$4.\quad p\quad iff\quad q\\ \equiv (p\rightarrow q)\wedge (q\rightarrow p)$$

I think #3 is wrong but I'm not sure why.

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# Difference between only if and if and only if

**Physics Forums | Science Articles, Homework Help, Discussion**