Conditional statement (logic): Difference between revisions

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{{Expert-subject|Mathematics|date=January 2012}}

{{Wikify|date=January 2012}}

In [[philosophy]], [[logic]], and [[mathematics]], a '''conditional statement''' is a [[proposition]] that can be written in the form "If ''p'', then ''q''," where ''p'' and ''q'' are propositions. The proposition immediately following the word "if" is called the hypothesis (also called antecedent). The proposition immediately following the word "then" is called the conclusion (also called consequence). In the aforementioned form for conditional statements, ''p'' is the hypothesis and ''q'' is the conclusion. A conditional statement is often called simply a '''conditional''' (also called an '''implication'''). Unlike the [[material conditional]], a conditional statement need not be truth-functional.<ref>Hardegree 1994, p. 41-44</ref> Conditional statements are often [[symbolic logic|symbolized]] using an arrow (→) as ''p'' → ''q'' (read "''p'' implies ''q''"). The conditional statement in symbolic form is as follows:

* <math>p \rightarrow q</math>

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== References ==

* Hardegree, Gary. ''Symbolic Logic: A First Course (2nd Edition)''. UMass Amherst Department of Philosophy, n.d. Web. 18 December 2011 <http://courses.umass.edu/phil110-gmh/text.htm>.

* Larson, Ron, Laurie Boswell, and Lee Stiff. ''Geometry''. Boston: McDougal Littell, 2001. Print.

* Larson, Ron, Laurie Boswell, Timothy D. Kanold, and Lee Stiff. ''Geometry''. Boston: McDougal Littell, 2007. Print.