Question

what is the contrapositive of the statement?

all squares are rectangles.

if a figure is a square, then it is a rectangle.
if a figure is a rectangle, then it is a square.
if a figure is not a square, then it is not a rectangle.
if a figure is not a rectangle, then it is not a square.

Explanation:

Convert the statement to conditional form

The statement "All squares are rectangles" can be written as:
If a figure is a square, then it is a rectangle.
Here, the hypothesis \(p\) is "a figure is a square" and the conclusion \(q\) is "it is a rectangle".

Apply the contrapositive rule

The contrapositive of a conditional statement \(p
ightarrow q\) is \(
eg q
ightarrow
eg p\).
Negating the conclusion \(q\) gives: "a figure is not a rectangle".
Negating the hypothesis \(p\) gives: "it is not a square".
Combining these gives: "If a figure is not a rectangle, then it is not a square."

Match with the given options

The fourth option matches this statement exactly.

Answer:

• If a figure is a square, then it is a rectangle.
• If a figure is a rectangle, then it is a square.
• If a figure is not a square, then it is not a rectangle.
• If a figure is not a rectangle, then it is not a square. (Correct answer)