In propositional logic, biconditional introduction is a valid rule of inference. It allows for one to infer a biconditional from two conditional statements. The rule makes it possible to introduce a biconditional statement into a logical proof. If is true, and then one may infer that is true. For example, from the statements "if I'm breathing, then I'm alive" and "if I'm alive, then I'm breathing", it can be inferred that "I'm breathing if and only if I'm alive". Biconditional introduction is the converse of biconditional elimination. The rule can be stated formally as:
where the rule is that wherever instances of "" and "" appear on lines of a proof, "" can validly be placed on a subsequent line.
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Famous quotes containing the word introduction:
“The role of the stepmother is the most difficult of all, because you can’t ever just be. You’re constantly being tested—by the children, the neighbors, your husband, the relatives, old friends who knew the children’s parents in their first marriage, and by yourself.”
—Anonymous Stepparent. Making It as a Stepparent, by Claire Berman, introduction (1980, repr. 1986)