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Biconditional

p \leftrightarrow q

Given statement variables p and q, the biconditional of p and q is “p if, and only if, q.” If both p and q have the same truth values the statement is true, and it is false if p and q have opposite truth values.

\displaystyle p

\displaystyle q

\displaystyle p \leftrightarrow q

T T T
T F F
F T F
F F T