Let's analyze the given logical statement and its different forms step-by-step.
### Original Statement
The original statement is:
"If a figure is a polygon, then it is a quadrilateral."
### Converse
The converse of the statement is formed by reversing the hypothesis and conclusion of the original statement:
"If a figure is a quadrilateral, then it is a polygon."
To evaluate this, we need to check whether all quadrilaterals (four-sided figures) are polygons.
- A quadrilateral always has four sides and satisfies the definition of a polygon, which is a closed figure with three or more straight sides.
Thus, the converse is true.
### Inverse
The inverse of the statement is formed by negating both the hypothesis and conclusion of the original statement:
"If a figure is not a polygon, then it is not a quadrilateral."
To evaluate this, we need to consider if a figure that is not a polygon (i.e., does not have three or more straight sides) could possibly be a quadrilateral.
- Any figure that is not a polygon cannot have any closed structure with straight sides, much less four sides. Hence, it cannot be a quadrilateral.
Thus, the inverse is true.
### Contrapositive
The contrapositive of the statement is formed by both reversing and negating the hypothesis and conclusion of the original statement:
"If a figure is not a quadrilateral, then it is not a polygon."
For this, we need to check if figures outside of being quadrilaterals (i.e., figures either with less than or more than four sides) can be polygons.
- Many polygons exist that are not quadrilaterals, such as triangles (3 sides), pentagons (5 sides), hexagons (6 sides), etc.
Thus, the contrapositive is false.
So, the evaluation for the given logical statement would be:
- Converse: True
- Inverse: True
- Contrapositive: False
These analyses confirm the results.
