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A gardener knows that if it rains, the garden will be watered. It is raining. What conclusion can he make?

Deductive Reasoning. LESSON 2-3. Additional Examples. A gardener knows that if it rains, the garden will be watered. It is raining. What conclusion can he make?. The first sentence contains a conditional statement. The hypothesis is “It rains.”

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A gardener knows that if it rains, the garden will be watered. It is raining. What conclusion can he make?

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  1. Deductive Reasoning LESSON 2-3 Additional Examples A gardener knows that if it rains, the garden will be watered. It is raining. What conclusion can he make? The first sentence contains a conditional statement. The hypothesis is “It rains.” Because the hypothesis is true, the gardener can conclude that the garden will be watered. Quick Check

  2. Deductive Reasoning LESSON 2-3 Additional Examples For the given statements, what can you conclude? Given: If A is acute, mA < 90. A is acute. A conditional and its hypothesis are both given as true. By the Law of Detachment, you can conclude that the conclusion of the conditional mA < 90 is also true. Quick Check

  3. Deductive Reasoning LESSON 2-3 Additional Examples Does the following argument illustrate the Law of Detachment? Given: If you make a field goal in basketball, you score two points.Jenna scored two points in basketball. You conclude: Jenna made a field goal. The two given statements mean that a conditional and its conclusion are both true. The Law of Detachment applies only if a conditional and its hypothesis are true. You can make no conclusion. You cannot conclude that Jenna made a field goal. Quick Check

  4. Deductive Reasoning LESSON 2-3 Additional Examples Use the Law of Syllogism to draw a conclusion from the following true statements: If a quadrilateral is a square, then it contains four right angles. If a quadrilateral contains four right angles, then it is a rectangle. The conclusion of the first conditional is the hypothesis of the second conditional. This means that you can apply the Law of Syllogism. The Law of Syllogism: If pq and qr are true, then pr is a true statement. So you can conclude: If a quadrilateral is a square, then it is a rectangle. Quick Check

  5. Deductive Reasoning LESSON 2-3 Additional Examples Use the Laws of Detachment and Syllogism to draw a possible conclusion. If the circus is in town, then there are tents at the fairground. If there are tents at the fairground, then Paul is working as a night watchman. The circus is in town. Because the conclusion of the first statement is the hypothesis of the second statement, you can apply the Law of Syllogism to write this new conditional: If the circus is in town, then Paul is working as a night watchman. The third statement means that the hypothesis of the new conditional is true. You can use the Law of Detachment to form the conclusion: Paul is working as a night watchman. Quick Check

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