Question

what is the contrapositive of the statement? all squares are rectangles. \bigcirc if a figure is a square, then it is a rectangle. \bigcirc if a figure is a rectangle, then it is a square. \bigcirc if a figure is not a square, then it is not a rectangle. \bigcirc if a figure is not a rectangle, then it is not a square.

Explanation:

To find the contrapositive of a conditional statement \( p \to q \) (where \( p \) is the hypothesis and \( q \) is the conclusion), we use the rule: the contrapositive is \(
eg q \to
eg p \).

First, rewrite "All squares are rectangles" as a conditional statement: "If a figure is a square (\( p \)), then it is a rectangle (\( q \))".

Now, find \(
eg q \) (not a rectangle) and \(
eg p \) (not a square). The contrapositive should be "If a figure is not a rectangle (\(
eg q \)), then it is not a square (\(
eg p \))".

Let's analyze the options:

• Option 1: This is the original conditional statement, not the contrapositive.
• Option 2: This is the converse (swapping \( p \) and \( q \)), not the contrapositive.
• Option 3: This is the inverse (negating both \( p \) and \( q \) but not reversing them), not the contrapositive.
• Option 4: This matches \(

eg q \to
eg p \), so it is the contrapositive.

Answer:

D. If a figure is not a rectangle, then it is not a square.