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.
A. You have a quadrilateral.
B. You have a rectangle.
C. Squares and rectangles are the same.
D. All sides are the same length.
Answer (2)
The problem provides a conditional statement: If you have a square, then you have a rectangle.
We are given that we have a square.
Applying the law of detachment, which states that if 'If p, then q' is true and p is true, then q is true.
Conclude that we have a rectangle: You have a rectangle.
Explanation
Problem Analysis We are given the conditional statement: If you have a square, then you have a rectangle. We are also given that we have a square. We need to apply the law of detachment to determine the conclusion.
Law of Detachment The law of detachment states that if a conditional statement 'If p, then q' is true, and p is true, then q is true. In this case, p is 'you have a square' and q is 'you have a rectangle'.
Applying the Law Since we are given that we have a square (p is true), and the conditional statement 'If you have a square, then you have a rectangle' is true, we can conclude that we have a rectangle (q is true).
Examples
The law of detachment is used in everyday reasoning. For example, if a store advertises 'If you spend over $50, you get free shipping,' and you spend $60, you can conclude you get free shipping. This logical deduction helps in making decisions based on given conditions.
By applying the law of detachment to the statement "If you have a square, then you have a rectangle," we conclude that since we have a square, we also have a rectangle. Therefore, the correct answer is B. You have a rectangle.
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