Question

given statements:
\if a shape has four sides, then it is a quadrilateral.\
\a square has four sides.\
which is a logical conclusion from the given statements?
a square has opposite angles that are congruent.
a square is a quadrilateral.
all shapes can be a quadrilateral.
a square has opposite sides that are congruent.

Explanation:

Step1: Analyze the first statement

The first statement is a conditional: if a shape has four sides (let \(p\) be "a shape has four sides"), then it is a quadrilateral (let \(q\) be "it is a quadrilateral"), written as \(p
ightarrow q\).

Step2: Analyze the second statement

The second statement is \(p\) (a square has four sides, so for the square, \(p\) is True).

Step3: Apply modus ponens

By the rule of modus ponens (\((p
ightarrow q)\land p\Rightarrow q\)), since \(p\) (a square has four sides) and \(p
ightarrow q\) (if a shape has four sides, then it is a quadrilateral), we can conclude \(q\) for the square.

Answer:

A square is a quadrilateral.