Explain Bi-conditional.

A biconditional, also known as a double implication, is a logical connective that represents a relationship between two propositions where both are true or false simultaneously. The symbol used for the biconditional is "↔," and it is read as "if and only if" or "iff."

The biconditional statement "P ↔ Q" asserts that proposition P is true if and only if proposition Q is true. It encompasses two implications: if P is true, then Q must be true, and if Q is true, then P must be true. If both propositions have the same truth value (both true or both false), the biconditional statement is true; otherwise, it is false.

Symbolically:

• (P \leftrightarrow Q) is true when both (P \rightarrow Q) and (Q \rightarrow P) are true.
• (P \leftrightarrow Q) is false when (P \rightarrow Q) is true and (Q \rightarrow P) is false or vice versa.

In everyday language, a biconditional is often expressed as "P if and only if Q," emphasizing the mutual dependence of the two propositions. Biconditionals are widely used in mathematics, logic, and philosophy to express equivalence and mutual exclusivity between statements.