Question

which statement is true about this argument?
premises:
if a quadrilateral is a square, then the quadrilateral has four right angles.
quadrilateral ( j k l m ) has four right angles.
conclusion:
quadrilateral ( j k l m ) is a square.
the argument is not valid because the conclusion does not follow from the premises.
the argument is valid by the law of syllogism.
the argument is valid by the law of detachment.
the argument is not valid because the premises are not true

Explanation:

Step1: Analyze the law of detachment

The law of detachment states that if \(p
ightarrow q\) (if \(p\) then \(q\)) and \(p\) is true, then \(q\) is true. Here, the first premise is \(p
ightarrow q\) (if a quadrilateral is a square (\(p\)), then it has four right angles (\(q\))). The second premise is \(q\) (quadrilateral \(JKLM\) has four right angles). We do not have \(p\) (the quadrilateral is a square) as a premise.

Step2: Analyze the law of syllogism

The law of syllogism is \((p
ightarrow q)\land(q
ightarrow r)
ightarrow(p
ightarrow r)\). There is only one conditional statement here, so the law of syllogism does not apply.

Step3: Check premise truth - value

The first premise “If a quadrilateral is a square, then the quadrilateral has four right angles” is a true geometric statement. A square is a type of quadrilateral with four right angles. The second premise “Quadrilateral \(JKLM\) has four right angles” can be a true statement (e.g., a rectangle also has four right angles). But the conclusion “Quadrilateral \(JKLM\) is a square” is not necessarily true. A rectangle (a non - square quadrilateral) also has four right angles. So the conclusion does not follow from the premises.

Answer:

The argument is not valid because the conclusion does not follow from the premises.