Material conditional
Semantics

From a classical semantic perspective, material implication is the binary truth functional operator which returns "true" unless its first argument is true and its second argument is false. This semantics can be shown graphically in a truth table such as the one below. One can also consider the equivalence A → B ≡ ¬ (A ∧ ¬ B) ≡ ¬ A ∨ B {\displaystyle A\to B\equiv \neg (A\land \neg B)\equiv \neg A\lor B}.
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