Question

Which of the following best describes the error in interpreting the statement below?

If a figure is a rectangle, then the figure has four sides.
A trapezoid has four sides.
Using the Law of Detachment, you can
conclude that a trapezoid is a rectangle."

A) The statement incorrectly assumes that all figures with four sides are rectangles.

B) The statement misapplies the Law of Detachment in concluding the trapezoid is a rectangle.

C) The statement erroneously asserts that all trapezoids are rectangles.

D) The statement fails to provide sufficient information to draw any conclusions about the relationship between trapezoids and rectangles.

Answer 1

The error in interpreting the statement is that the statement misapplies the Law of Detachment in concluding that a trapezoid is a rectangle.

Step-by-step explanation:

The error in interpreting the statement is option B: The statement misapplies the Law of Detachment in concluding that a trapezoid is a rectangle.

In the given statement, it is true that if a figure is a rectangle, then it has four sides. However, the statement incorrectly applies the Law of Detachment to conclude that a trapezoid, which also has four sides, is a rectangle. The Law of Detachment states that if a conditional statement is true and the hypothesis is true, then the conclusion is also true. In this case, the hypothesis is true (a trapezoid has four sides), but it does not guarantee that the conclusion (a trapezoid is a rectangle) is true.

Therefore, the correct choice is B: The statement misapplies the Law of Detachment in concluding the trapezoid is a rectangle.