Biconditional/IF AND ONLY IF

This lecture explains our final logical operation: the biconditional.

Takeaway Points

1. A biconditional represents the English expression “if and only if.” We represent it with <=>.
2. It is the logical equivalent to the equals sign from algebra. It says that if one part is true, the other is true as well, and if one is false, the other is false as well.
3. Like the conditional operator, the biconditional operator is notationally redundant. P <=> Q could also be written as (P => Q) ^ (Q => P).
4. Some people use “if and only if” in English as a fancy way of saying “if.” These are not the same thing. Don’t confuse the two, or a logician will judge you.

Back to Logic 101