2.1.3 Using Deductive Reasoning to Verify Conjectures − Practice

1. A student looks at the sequence 1, 2, 4, 7, 11, 16, 22 and determines that the next two numbers in the sequence are 29 and 37. Does the conclusion use inductive or deductive reasoning?

2. Determine if the following conjecture is valid. Given: If a computer sales person sells at least 10 computers in a week, then he gets a bonus. Jerry sells 12 computers in a week. Conclusion: Jerry gets a bonus.

3. Determine if the following conjecture is valid.

4. Determine if the following conjecture is valid. Given: If x is an odd number, then x is an integer. If x is an integer, then x is a rational number. 19.132 is a rational number. Conclusion: 19.132 is an odd number.

Given: For the past five years, Robyn has grown 2 in. every year. She is now 15 years old and is 5 ft, 4 in. tall. Conclusion: Robyn will be 6 ft, 2 in. tall when she’s 22 years old.

5. Determine if the following conjecture is valid. Given: If x is a prime number, then x is an integer. If x is an integer, then x is a rational

6. Which Law deals with the truth value of p and q ?

○ Law of Deduction ○ Law of Detachment ○ Law of Syllogism ○ Law of Separation

number. 12 is a rational number. Conclusion: 12 is a prime number.

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