Logical Symbols (2011)

The symbol is used to symbolize a relationship called material implication; a compound statement formed with this connective is true unless the component on the left (the antecedent) is true and the component on the right (the consequent) is false, as shown in the truth-table at the right. Finally, the is used to symbolize material equivalence, in which the compound statement is true only when its component statements have the same truth-value—either both are true or both are false. This corresponds to a minimal interpretation of the biconditional statements commonly expressed in English with the connective phrase ” . . . if and only if . . . .”

In compound statements formed with the five truth-functional connectives, one important logical feature remains the same.

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