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Big Ideas Math Integrated I, 2016 View details

2. Inductive and Deductive Reasoning

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Exercise 35 Page 457

Does the Law of Detachment evaluate a conditional statements hypothesis or conclusion?

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Let's identify the hypothesis p and conclusion q of the conditional statement. if a figure is a rectangle, then the figure has four sides. The Law of Detachment states that if the hypothesis is true, then the conclusion is also true. However, the third sentence states that a trapezoid has four sides, which matches the conclusion of the conditional statement. Therefore, the Law of Detachment cannot be used to say anything about the hypothesis.