# Inverse of a mathematical statement.

If the quadrilateral ABCD is a parellelogram with one right angle , then the quadrilateral ABCD is a rectangle.

What is the inverse statement of the above statement?

1. If the quadrilateral ABCD is not a parellelogram with one right angle ,then the quadrilateral ABCD is a rectangle.
2. If the quadrilateral ABCD is a parellelogram with no right angle ,then the quadrilateral ABCD is a rectangle.
3. Both
• By "inverse", do you mean "negation"? If so, then to negate a statement (A implies B), first write that statement in the form (not A) or B. Now negate it using DeMorgan's Laws: not [ (not A) or B ] = A and (not B).
– avs
Jul 19 '17 at 19:40

Inverse:

If the quadrilateral $ABCD$ is not a parallelogram with one right angle, then the quadrilateral $ABCD$ is not a rectangle.

p = the quadrilateral $ABCD$ is a parallelogram with one right angle

q = the quadrilateral $ABCD$ is a rectangle

if $(not)p$ then $(not)q$

Keep these three distinct, but related, notions in mind:

If the original statement is 'If P then Q', then:

The Inverse is: 'If not P then not Q'

The Converse is: 'if Q then P'

The Contrapositive is: 'if not Q then not P'

Note that:

• The Inverse and the Converse are not equivalent, and also not implied by the original.
• The Contrapositive is equivalent (and therefore is implied by, as well as implies, to the original.
• A statements' Inverse is equivalent to its Converse (not the same, but equivalent)
• The Inverse of the Converse of any statement is the Contrapositive of statement. Same for the Converse of the Inverse.