Question

select the correct answer.
given statements:
if a shape is a rhombus, then the diagonals are perpendicular.
a square is a rhombus.
what is a logical conclusion from the given statements?
a. the sides of a square are perpendicular.
b. the diagonals of a square are perpendicular.
c. a rhombus is a square.
d. the diagonals of a square are not perpendicular.

Explanation:

Step1: Analyze the first statement

The first statement is “If a shape is a rhombus, then the diagonals are perpendicular”. Let \(p\) be “a shape is a rhombus” and \(q\) be “the diagonals are perpendicular”. So, we have \(p
ightarrow q\).

Step2: Analyze the second statement

The second statement is “A square is a rhombus”. So, for a square, \(p\) (the property of being a rhombus) is True.

Step3: Apply the law of detachment

By the law of detachment (\(p
ightarrow q\) and \(p\) is True, then \(q\) is True). Since a square is a rhombus (\(p\) is True for a square) and if a shape is a rhombus then its diagonals are perpendicular (\(p
ightarrow q\)), we can conclude that for a square (which is a rhombus), the diagonals are perpendicular.

Answer:

B. The diagonals of a square are perpendicular.