Question

(b) problem 11: (first taught in lesson 48) read the false statement below and then tell whether its converse, inverse, and contrapositive are true. if a figure is a polygon, then it is a triangle. converse inverse contrapositive if a figure is a triangle, then it is a polygon. true false

Explanation:

Step1: Find the inverse

The original statement is “If \(p\) (a figure is a polygon), then \(q\) (it is a triangle)”. The inverse is “If not \(p\), then not \(q\)”, which is “If a figure is not a polygon, then it is not a triangle”. A triangle is a polygon. If a figure is not a polygon, it can't be a triangle. But the original statement's inverse is formed by negating the hypothesis and conclusion. The inverse is false because there are non - polygon figures (e.g., a circle) and non - triangle non - polygons.

Step2: Find the contrapositive

The contrapositive is “If not \(q\), then not \(p\)”. The contrapositive of “If a figure is a polygon, then it is a triangle” is “If a figure is not a triangle, then it is not a polygon”. But there are polygons that are not triangles (e.g., quadrilaterals). So the contrapositive is false.

Answer:

Inverse: False; Contrapositive: False