Conditional statement (logic): Difference between revisions

Revision as of 16:44, 23 January 2012

Revision as of 12:09, 4 February 2012

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

As a proposition, a conditional statement is either [[truth|true]] or false. A conditional statement is true [[if and only if]] the conclusion is true in every case that the hypothesis is true. A conditional statement is false if and only if a [[counterexample]] to the conditional statement exists. A counterexample to a conditional statement exists if and only if there is a case in which the hypothesis is true, but the conclusion is false. A counterexample(which is to say, a specialconditional statement is true whenever the antecedent is false, or when the consequent and typeantecedent ofare possibleboth casetrue).

Examples of conditional statements include: