Question

assume that the set of given information is true. use this set of information and deductive reasoning to write a conclusion about the situation. if a rectangle has diagonals that are perpendicular to each other, then the rectangle is a square. the rectangle has diagonals that are perpendicular to each other. choose the correct answer below. a. if a square has diagonals that are perpendicular to each other, then the square is a rectangle. b. the square is a rectangle. c. all squares are rectangles. d. the rectangle is a square. e. all rectangles are squares.

Explanation:

We are given a conditional statement: "If a rectangle has diagonals that are perpendicular to each other, then the rectangle is a square" and the fact that "The rectangle has diagonals that are perpendicular to each other". By modus ponens (a form of deductive reasoning where if we have a statement "If P, then Q" and we know P is true, we can conclude Q), since the rectangle satisfies the condition (P: rectangle has perpendicular diagonals) of the conditional, we can conclude Q: the rectangle is a square.

Option A is a different conditional statement and not the conclusion from the given info. Option B is about a square being a rectangle, which is not the conclusion here. Option C is a general statement about all squares and rectangles, not derived from the given specific rectangle. Option E is false as not all rectangles are squares. Only option D follows from the given premises.

Answer:

D. The rectangle is a square.