What is a Biconditional?

A biconditional is a statement of the form "if and only if" (shortened to "iff"). It is a logical connective that combines two statements and implies that they are equivalent, meaning that one statement is true if and only if the other statement is true.

For example, the biconditional "If it rains, then the streets will be wet" can be written in symbolic form as:

P → Q

where P represents "it rains" and Q represents "the streets will be wet". The arrow (→) indicates that P implies Q, meaning that if P is true, then Q must also be true.

In this case, the biconditional statement says that if it rains, then the streets will be wet, but it does not say that the streets will be wet simply because it rains. Instead, it says that the two statements are equivalent, and one cannot be true without the other being true.