Question

determine whether the conclusion is valid based on the given information. select valid or invalid. explain your reasoning. given: if a figure is a square, then it has four right angles. figure abcd has four right angles. conclusion: figure abcd is a square. select choice v select choice

Explanation:

Step1: Analyze the Given Statement

The given statement is a conditional: "If a figure is a square, then it has four right angles." This means being a square (let's call this \( P \)) implies having four right angles (let's call this \( Q \)), so \( P
ightarrow Q \).

Step2: Analyze the Conclusion

The conclusion is "Figure \( ABCD \) is a square" (which is \( P \)) because "Figure \( ABCD \) has four right angles" (which is \( Q \)). So we are using \( Q \) to conclude \( P \), which is the fallacy of affirming the consequent. Just because a figure has four right angles ( \( Q \) is true), it doesn't mean it's a square ( \( P \) is true). For example, a rectangle has four right angles but isn't necessarily a square.

Step3: Determine Validity

Since the reasoning is affirming the consequent (using the consequent of the conditional to conclude the antecedent), the conclusion is not valid. The given information only tells us that squares have four right angles, not that all figures with four right angles are squares.

Answer:

The conclusion is invalid. The reasoning commits the fallacy of affirming the consequent: knowing a figure has four right angles (the consequent of the conditional "If a square, then four right angles") does not guarantee it is a square (the antecedent), as other figures (e.g., rectangles) can have four right angles.