Vacuously True Statements

Learning Objectives: Determine when a conditional statement is vacuously true

A conditional statement of the form “if P then Q” is called vacuously true whenever P is false. This might seem counterintuitive, but consider the reverse. The conditional “if P then Q” is false whenever the assumption P is true and the conclusion Q is false. So when the assumption is false it doesn’t matter what the conclusion is, and we call the conditional true, but in a vacuous sense.

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This video was created by Dr. Trefor Bazett