In logic, conditioned disjunction (sometimes called conditional disjunction) is a ternary logical connective introduced by Church.

[1][2] Given operands p, q, and r, which represent truth-valued propositions, the meaning of the conditioned disjunction [p, q, r] is given by In words, [p, q, r] is equivalent to: "if q, then p, else r", or "p or r, according as q or not q".

In electronic logic terms, it may also be viewed as a single-bit multiplexer.

In conjunction with truth constants denoting each truth-value, conditioned disjunction is truth-functionally complete for classical logic.

[3] There are other truth-functionally complete ternary connectives.