Question

what conclusion can you draw from the following statements? - if a figure is a square, then it has four sides. - if a figure has four sides, then it is not a triangle. a. if a figure is not a triangle, then it is a square. b. if a figure has four sides, then it is a square. c. if a figure is a square, then it is not a triangle. d. if a figure is not a triangle, then it has four sides.

Explanation:

1. Analyze the given statements:

• Statement 1: If a figure is a square, then it has four sides (let's denote \( p \): figure is a square, \( q \): figure has four sides, so \( p

ightarrow q \)).

• Statement 2: If a figure has four sides, then it is not a triangle (let's denote \( q

ightarrow r \), where \( r \): figure is not a triangle).

• By the law of syllogism, if \( p

ightarrow q \) and \( q
ightarrow r \), then \( p
ightarrow r \).

1. Evaluate each option:

• Option A: Just because a figure is not a triangle (\( r \)), we can't conclude it's a square (\( p \)). There are other figures with four sides (like rectangles, parallelograms) or more/less sides that are not triangles. So A is incorrect.
• Option B: Having four sides (\( q \)) doesn't mean it's a square. There are many quadrilaterals (e.g., rectangles, trapezoids) that are not squares. So B is incorrect.
• Option C: From the syllogism, if a figure is a square (\( p \)), then it has four sides (\( q \)) and if it has four sides (\( q \)), then it's not a triangle (\( r \)). So if a figure is a square, then it is not a triangle (\( p

ightarrow r \)). This is correct.

• Option D: Just because a figure is not a triangle (\( r \)), we can't conclude it has four sides. A pentagon is not a triangle and has five sides. So D is incorrect.

Answer:

C. If a figure is a square, then it is not a triangle