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: Define the original statement

Original statement: If \(p\) (a figure is a polygon), then \(q\) (it is a triangle). \(p
ightarrow q\) (False, since not all polygons are triangles).

Step2: Find the converse

Converse: If \(q\), then \(p\). \(q
ightarrow p\). A triangle is a polygon. So, \(q
ightarrow p\) is True.

Step3: Find the inverse

Inverse: If \(
eg p\), then \(
eg q\). \(
eg p
ightarrow
eg q\). If a figure is not a polygon (\(
eg p\)), then it is not a triangle (\(
eg q\)). This is True (because a non - polygon can't be a triangle).

Step4: Find the contrapositive

Contrapositive: If \(
eg q\), then \(
eg p\). \(
eg q
ightarrow
eg p\). If a figure is not a triangle (\(
eg q\)), then it is not a polygon (\(
eg p\)). This is False (e.g., a square is not a triangle but is a polygon).

Answer:

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