Question

1. assume that you have a square. what can you conclude from applying the law of detachment to this conditional? if you have a square, then you have a rectangle. all sides are the same length. squares and rectangles are the same. you have a rectangle. you have a quadrilateral.

Explanation:

The law of detachment states that if \(p
ightarrow q\) (if \(p\), then \(q\)) is a true conditional statement and \(p\) is true, then \(q\) is true. Here, \(p = \) "you have a square" and \(q=\) "you have a rectangle". Since we are given that \(p\) (we have a square) is true, by the law of detachment, \(q\) (we have a rectangle) must be true.

• The statement "All sides are the same length" is a property of a square, not a conclusion from the given conditional and the law of detachment.
• "Squares and rectangles are the same" is false. A square is a special - case rectangle (with all sides equal), but they are not identical in all aspects (a rectangle does not necessarily have all sides equal).
• "You have a quadrilateral" is a more general statement. While a square (and thus a rectangle) is a quadrilateral, it is not the conclusion directly from the given conditional \(p

ightarrow q\) and \(p\) (applying the law of detachment).

Answer:

You have a rectangle.