Which statement is true about this argument ? premises: if a quadrilateral is a square, then the quadrilateral is a rectangle. if a quadrilateral is a rectangle then the quadrilateral is a parallelogram. conclusion: if a quadrilateral is a square, then the quadrilateral is a parallelogram. a. the argument is not valid because the premises are not true. b. the argument is valid by the law of syllogism c. the argument is valid by the law of detachment d. the argument is not valid because the conclusion does not follow from the premises.

It's good to review the laws of syllogism and detachment.

Law of detachment:
Statement 1: If p then q.
Statement 2: p is true.
By the law of detachment, you can conclude "q is true."

Law of syllogism:
Statement 1: If p then q.
Statement 2: If q then r.
By the law of syllogism, you can conclude "If p then r."

Now look at which of the two cases above you have.
Statement 1: If a quadrilateral is a square, then the quadrilateral is a rectangle.
This is "if p then q."

Statement 2:
If a quadrilateral is a rectangle then the quadrilateral is a parallelogram.
This is "if q then r."

You have
If p then q.
If q then r.

This is what you need for the law of syllogism.

That means you can conclude "if p then r", which in this specific case is
"If a quadrilateral is a square, then the quadrilateral is a parallelogram."

The answer is that it is a valid argument by the law of syllogism.

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