The phrase "if and only if" (often abbreviated as "iff") is a logical connector used to indicate a biconditional relationship between two statements. This means that both statements are true at the same time or both are false. For example, the statement "A is true if and only if B is true" implies that A can only be true when B is true, and vice versa. In mathematics and logic, "if and only if" is crucial for defining concepts and theorems. For instance, a triangle is classified as an equilateral triangle triangle if and only if all its sides are equal. This precise language helps eliminate ambiguity and ensures clarity in reasoning and proofs.