Logic Laws and Logic Review

Front

What is a counterexample?

Back

A counterexample is an example that disproves a statement or proposition.

Front

What is the contrapositive of a statement?

Back

The contrapositive of a statement 'If P, then Q' is 'If not Q, then not P.'

Front

What is the inverse of a statement?

Back

The inverse of a statement 'If P, then Q' is 'If not P, then not Q.'

Front

What is the converse of a statement?

Back

The converse of a statement 'If P, then Q' is 'If Q, then P.'

Front

What is the Law of Detachment?

Back

The Law of Detachment states that if 'If P, then Q' is true and P is true, then Q must also be true.

Front

Provide an example of a counterexample for the statement: 'If a polygon is a quadrilateral, then it is a trapezoid.'

Back

A rectangle is a counterexample because it is a quadrilateral that is not a trapezoid.

Front

What is the relationship between quadrilaterals and trapezoids?

Back

Not all quadrilaterals are trapezoids; a trapezoid is a specific type of quadrilateral.

Front

How do you form the contrapositive of 'If it rains, then the ground is wet'?

Back

The contrapositive is 'If the ground is not wet, then it does not rain.'

Front

What is an example of the inverse of 'If a polygon is a triangle, then it has three sides'?

Back

The inverse is 'If a polygon is not a triangle, then it does not have three sides.'

Front

What is an example of the converse of 'If it is a dog, then it is an animal'?

Back

The converse is 'If it is an animal, then it is a dog.' (This is not necessarily true.)