Section Progress:

16.2 The Bionditional: ↔

"Biconditional" just means two conditionals. P↔Q just means P→Q and Q→P.

↔ is the biconditional; if and only if; iff.

The biconditional is the way we translate the phrase "if and only if", or "iff" for short.

Pia is guilty if and only if Quinn is guilty

is translated like this:

P↔Q

Now you try.

You can learn a lot about conditionals by realizing that if-and-only-if is not redundant. "P if and only if Q" says "P if Q" and "P only if Q", and those are not the same thing.

Another common expression from logic and mathematics translated with the biconditional is "just in case".

P just in case Q: P↔Q

P just in case Q: P↔Q

We don't claim, though, that the biconditional is always what is meant by "just in case" in English. Rather, we think that logicians got tired of saying "if and only if" all the time, and they now use "just in case" as a synonym for it.

We will follow this common practice, so if you see "just in case", use the biconditional.

17.2 The Biconditional: ↔