Question

1. \if a shape has exactly three sides, then the shape is a triangle.\ converse: if a shape ​​is a triangle , then the shape ​​has exactly three sides. inverse: if a shape ​​select, then the shape ​​select. contrapositive: if a shape ​​select, then the shape ​​select.

Explanation:

Step1: Recall logical statement forms

Given the original statement: "If \( p \), then \( q \)" where \( p \): "a shape has exactly three sides" and \( q \): "the shape is a triangle".

Step2: Determine Inverse form

The inverse of "If \( p \), then \( q \)" is "If \(
eg p \), then \(
eg q \)". So \(
eg p \): "a shape does not have exactly three sides", \(
eg q \): "the shape is not a triangle". Thus, Inverse: If a shape does not have exactly three sides, then the shape is not a triangle.

Step3: Determine Contrapositive form

The contrapositive of "If \( p \), then \( q \)" is "If \(
eg q \), then \(
eg p \)". So \(
eg q \): "a shape is not a triangle", \(
eg p \): "the shape does not have exactly three sides". Thus, Contrapositive: If a shape is not a triangle, then the shape does not have exactly three sides.

Answer:

• Inverse: If a shape does not have exactly three sides, then the shape is not a triangle. (So first "Select" for Inverse: "does not have exactly three sides", second "Select": "is not a triangle")
• Contrapositive: If a shape is not a triangle, then the shape does not have exactly three sides. (First "Select" for Contrapositive: "is not a triangle", second "Select": "does not have exactly three sides")