Geometry: Logic Statements

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Geometry: Logic Statements Variations on Conditional Statements

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Topics Geometry: Logic Statements Variations on Conditional Statements

The Contrapositive

The contrapositive of a statement is formed when the hypothesis and the conclusion are interchanged, and both are replaced by their negation. In other words, the contrapositive of a statement is the same as the inverse of that statement's converse, or the converse of its inverse.

Take the statement, "Long books are fun to read." Its contrapositive is "Books that aren't fun to read aren't long." The statement "if p, then q" becomes "if not q, then not p."

The contrapositive of a statement always has the same truth value as the original statement. Therefore, the contrapositive of a definition is always true. For example, the statement "A triangle is a three-sided polygon" is true. Its contrapositive, "A polygon with greater or less than three sides is not a triangle" is also true.

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