Converse, Inverse, and Contrapositive

Converse

The converse of a conditional statement reverses the hypothesis and conclusion, forming a statement of the form "If q, then p" from the original "If p, then q."

Inverse

The inverse of a conditional statement negates both the hypothesis and conclusion, forming a statement of the form "If not p, then not q" from the original "If p, then q."

Contrapositive

The contrapositive of a conditional statement negates and reverses the hypothesis and conclusion, forming a statement of the form "If not q, then not p" from the original "If p, then q."

What would be the converse of the conditional “If a figure is a square then it is a quadrilateral.”

If a figure is a quadrilateral, then it is a square.

What would be the inverse of the conditional “If a figure is a square then it is a quadrilateral.”

If a figure is not a square, then it is not a quadrilateral.

What would be the contrapositive of the conditional “If a figure is a square then it is a quadrilateral.”

If a figure is not a quadrilateral, then it is not a square.

Which of the three is logically equivalent to each other: converse, inverse, or contrapositive?

The inverse and converse are logically equivalent to each other. The contrapositive is logically equivalent to the conditional.

Biconditional

A statement that is true when both the conditional and its converse are true. It can be expressed in the form "P if and only if Q."

Is the inverse of the conditional “If a figure is a square, then it is a quadrilateral.” true or false?

False, because it could be a different quadrilateral such as a rectangle or kite.

Is the contrapositive of the conditional “if a figure is a square then it is not a quadrilateral” a true or false statement?

True, because if a square is a quadrilateral so when the figure is not a quadrilateral, it can’t be a square.