Question

problem 13:
(first taught in
lesson 56)
read the true statement below and then tell
whether the converse, inverse, and contrapositive
are also true.
if a figure is not a rectangle, then it is not
a square.
converse
inverse
contrapositive
if a figure is not a square, then it is not
a rectangle.

Explanation:

Step1: Recall definitions

Let \(p\): A figure is not a rectangle. \(q\): A figure is not a square. The original statement is \(p
ightarrow q\).
The converse is \(q
ightarrow p\). The inverse is \(
eg p
ightarrow
eg q\). The contrapositive is \(
eg q
ightarrow
eg p\).

Step2: Analyze converse

The converse “If a figure is not a square, then it is not a rectangle” is false. For example, a non - square rectangle (a rectangle that is not a square) exists.

Step3: Analyze inverse

The inverse “If a figure is a rectangle, then it is a square” is false. There are rectangles that are not squares.

Step4: Analyze contrapositive

The contrapositive “If a figure is a square, then it is a rectangle” is true. By definition, a square is a special type of rectangle (a rectangle with all sides equal).

Answer:

Converse: False. Inverse: False. Contrapositive: True.