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Logical Reasoning and Conclusion Making

Learn how to use the laws of detachment and syllogism to make valid conclusions in various situations. Examples and guided practice included.

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Logical Reasoning and Conclusion Making

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  1. a. If two segments have the same length, then they are congruent. You know that BC = XY. b. Mary goes to the movies every Friday and Saturday night. Today is Friday. a. Because BC = XYsatisfies the hypothesis of a true conditional statement, the conclusion is also true. So, BC=XY. EXAMPLE 1 Use the Law of Detachment Use the Law of Detachment to make a valid conclusion in the true situation. SOLUTION

  2. b. First, identify the hypothesis and the conclusion of the first statement.The hypothesis is “If it is Friday or Saturday night,” and the conclusion is “then Mary goes to the movies.” EXAMPLE 1 Use the Law of Detachment “Today is Friday” satisfies the hypothesis of the conditional statement, so you can conclude that Mary will go to the movies tonight.

  3. 1. If 90°< mR < 180°, then Ris obtuse. The measure of Ris 155°. Using the Law of Detachment, what statement can you make? ANSWER Ris obtuse for Examples 1 and 2 GUIDED PRACTICE

  4. 2. If Jenelle gets a job, then she can afford a car. If Jenelle can afford a car, then she will drive to school. Using the Law of Syllogism, what statement can you make ? ANSWER If Jenelle gets a job, then she will drive to school. for Examples 1 and 2 GUIDED PRACTICE

  5. 3. If you get an A or better on your math test, then you can go to the movies. If you go to the movies, then you can watch your favorite actor. ANSWER Law of Syllogism. for Examples 1 and 2 GUIDED PRACTICE State the law of logic that is illustrated. If you get an A or better on your math test, then you can watch your favorite actor.

  6. 4. Ifx > 12, thenx + 9 > 20. The value ofxis 14 Therefore,x + 9 > 20 ANSWER Law of Detachment for Examples 1 and 2 GUIDED PRACTICE

  7. o ANSWER m C + m D = 90 Use the Law of Syllogism to make a valid conclusion in the true situation. If water is at room temperature, then it is a liquid. If water is a liquid, then it is not frozen. 2. ANSWER If water is at room temperature, then it is not frozen. Daily Homework Quiz 1. Use the Law of Detachment to make a valid conclusion in the true situation. If two angles are complementary, then the sum of their measures is 90 . C and D are complementary. o

  8. a. Each time Monica kicks a ball up in the air, it returns to the ground. So the next time Monica kicks a ball up in the air, it will return to the ground. b. All reptiles are cold-blooded. Parrots are not cold-blooded. Sue’s pet parrot is not a reptile. EXAMPLE 4 Compare inductive and deductive reasoning Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your reasoning.

  9. a. Inductive reasoning, because a pattern is used to reach the conclusion. Deductive reasoning, because facts about animals and the laws of logic are used to reach the conclusion. b. EXAMPLE 4 Reasoning from a graph SOLUTION

  10. 3. Jeanine buys popcorn. ANSWER true; the Law of Syllogism If Jeanine goes to the movies, Joaquin goes to the movies. 4. ANSWER False; no laws of logic apply. Daily Homework Quiz Use the true statements below to determine whether the conclusion is true or false. Explain your reasoning. If Jeanine does her homework, then she goes to the movies. If Joaquin goes to the movies, then he buys popcorn. If Jeanine goes to the movies, then she buys popcorn. Jeanine does her homework.

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