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# Biconditional (if-and-only-if)

_{ Jan 01 . 1970 }

Any two propositions **P** and **Q** can be joined with the biconditional operator, producing the new, complex, proposition:

**P if and only if Q**

The proposition **P if and only if Q** is true if and only if both **P** and **Q** are true, or if both **P** and **Q** are false. It is false only when one of them is true and the other false.