Question

write the statement in the form \if p, then q.\
a heptagon is a polygon with 7 sides.

choose the correct \if p, then q\ form of the given statement.
○ a. if a figure has 7 sides, then it is a heptagon.
○ b. if a heptagon is a polygon, then it has 7 sides.
○ c. if a figure is a heptagon, then it is a polygon with 7 sides.
○ d. if a figure is not a heptagon, then it does not have 7 sides.

Explanation:

The original statement defines a heptagon as a polygon with 7 sides. In an "if p, then q" statement, p is the condition and q is the conclusion. Here, the condition (p) is "a figure is a heptagon" and the conclusion (q) is "it is a polygon with 7 sides".

• Option A: The condition and conclusion are reversed. A figure with 7 sides could be other polygons (though in common definition, heptagon is 7 - sided polygon, but the original statement's structure is about heptagon's definition).
• Option B: The statement "a heptagon is a polygon" is redundant as the original statement is about the side - count of a heptagon.
• Option C: Correctly maps the condition (being a heptagon) to the conclusion (being a polygon with 7 sides) as per the original definition.
• Option D: The contrapositive is not in line with the direct definition given in the original statement.

Answer:

C. If a figure is a heptagon, then it is a polygon with 7 sides.