Minecraft wiki entry for Logic, associated text: An IMPLY gate (A → B) turns on either if both inputs are on, or if the first input is off. Unlike the other gates here, the inputs are not interchangeable; it is not commutative. This represents material implication or a conditional statement, "if A then B", or "A implies B". The output is off only if the antecedent A is true, but the consequent B is false. It is the logical equivalent of B ∨ ¬A, and the mathematical equivalent of A ≤ B.