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A logical proposition of the type "if P then Q", connecting two simple propositions P (the antecedent) and Q (the consequent). In the form used in mathematical logic the two propositions don't need to be connected. This is called material implication – an example is "if the Earth is flat then gold is a metal". A material implication is false only when the antecedent is true and the consequent false, otherwise it is true.

In normal discourse formal implication is used, in which the simple propositions are related in meaning; for example, "if it does not rain, we will go for a walk."

An implication is written as PQ, read "P implies Q."

Related category

   • LOGIC