What is a biconditional statement

what is a biconditional statement

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Conditional Statements

A conditional statement is any statement of the form “If P, then Q,” where P and Q are simple statements. P is called “the hypothesis,” and Q is called “the conclusion.” If you use the definitions of the previous examples of P and Q, “If P, then Q” means “If this figure is a triangle, then it has three sides.”

Deriving New Conditional Statements

Given any conditional statement, you can always derive three other conditional statements from it, for a total of four distinct types: the original statement, its “converse,” its “inverse” and its “contrapositive.”

The Converse of a Conditional Statement

To construct the converse of “If P, then Q,” you would simply exchange P for Q, thus obtaining “If Q, then P,” which here means “If this figure has three sides, then it is a triangle.” If a conditional statement is true, then its converse may be true, but it is not necessarily true. For example, it may be true that “If there is a major snowstorm, then they will cancel school.” But this clearly does not make it true that “If they cancel school, then there will be a major snowstorm.”

The Inverse of a Conditional

Statement

To construct the inverse of “if P, then Q,” you simply negate P and Q, thus obtaining “If not P, then not Q,” which here means “If this figure is not a triangle, then it does not have three sides.” If a conditional statement is true, then its inverse may be true, but it is not necessarily true. Return to the statement “If there is a major snowstorm, then they will cancel school.” Clearly, this does not make it true that “If there is no major snowstorm, then they will not cancel school” because school could be canceled for some other reason, such as a flood.

The Contrapositive of a Conditional Statement

To construct the contrapositive of “If P, then Q,” you either take the inverse of the converse, or the converse of the inverse, thus obtaining “if not Q, then not P,” which here means “If this figure does not have three sides, then it is not a triangle.” If a conditional statement is true, then its contrapositive is necessarily true as well. The fact that “If there is a major snowstorm, then they will cancel school” clearly makes it true that “If they do not cancel school, then no major snowstorm will have occurred.”

Source: ehow.com

Category: Forex

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