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A logical operator denoting logical equivalence or "if and only if" in mathematical proofs and logical statements.

\Leftrightarrow image

Examples

Logical equivalence

A⇔B means ’A if and only if B’A \Leftrightarrow B \text{ means 'A if and only if B'}
A \Leftrightarrow B \text{ means 'A if and only if B'}

Mathematical definition

x is even⇔x=2k for some k∈Zx \text{ is even} \Leftrightarrow x = 2k \text{ for some } k \in \mathbb{Z}
x \text{ is even} \Leftrightarrow x = 2k \text{ for some } k \in \mathbb{Z}

Set equality definition

A=B⇔(x∈A⇔x∈B)A = B \Leftrightarrow (x \in A \Leftrightarrow x \in B)
A = B \Leftrightarrow (x \in A \Leftrightarrow x \in B)