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2. Decide whether the arguments are valid. Explain. a. All math is fun. Logic is math. Logic is fun. b. If I exercise, then I will be tired. I do not exercise. Therefore, I am not tired. c. All natural numbers are integers. All integers are rational numbers. is not a rational number. is not an integer. d. All multiples of 2 are even. 18 is a multiple of 3. 18 is even. 3. In the book, the Rule of Detachment and the Chain rule have accompanying truth tables. In these truth tables, they mark the rows which justify these two rules. Do the same for the Rule of Contrapositive.

2. Decide whether the arguments are valid. Explain. a. All math is fun. Logic is math. Logic is fun. b. If I exercise, then I will be tired. I do not exercise. Therefore, I am not tired. c. All natural numbers are integers. All integers are rational numbers. is not a rational number. is not an integer. d. All multiples of 2 are even. 18 is a multiple of 3. 18 is even. 3. In the book, the Rule of Detachment and the Chain rule have accompanying truth tables. In these truth tables, they mark the rows which justify these two rules. Do the same for the Rule of Contrapositive.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve this problem 2 and 3 accordingly to example 8
Example 8 Use a Venn diagram to determine whether the following argument is valid or invalid. All serious environmentalists support Senate Bill 137. Senator Snodgrass supports Senate Bill 137. Therefore, it is clear that Senator Snodgrass is a serious environmentalist. Solution Let E represent people who are serious environmentalists. All of these people support Senate Bill 137 (C). But as Figure 5 indicates, Senator Snodgrass (S) may support Senate Bill 137 (C) without necessarily being inside E. Therefore, the argument is not valid. E Figure 5 с
Transcribed Image Text:Example 8 Use a Venn diagram to determine whether the following argument is valid or invalid. All serious environmentalists support Senate Bill 137. Senator Snodgrass supports Senate Bill 137. Therefore, it is clear that Senator Snodgrass is a serious environmentalist. Solution Let E represent people who are serious environmentalists. All of these people support Senate Bill 137 (C). But as Figure 5 indicates, Senator Snodgrass (S) may support Senate Bill 137 (C) without necessarily being inside E. Therefore, the argument is not valid. E Figure 5 с
2. Decide whether the arguments are valid. Explain. a. All math is fun. Logic is math. Logic is fun. b. If I exercise, then I will be tired. I do not exercise. Therefore, I am not tired. c. All natural numbers are integers. All integers are rational numbers. is not a rational number. is not an integer. d. All multiples of 2 are even. 18 is a multiple of 3. 18 is even. 3. In the book, the Rule of Detachment and the Chain rule have accompanying truth tables. In these truth tables, they mark the rows which justify these two rules. Do the same for the Rule of Contrapositive.
Transcribed Image Text:2. Decide whether the arguments are valid. Explain. a. All math is fun. Logic is math. Logic is fun. b. If I exercise, then I will be tired. I do not exercise. Therefore, I am not tired. c. All natural numbers are integers. All integers are rational numbers. is not a rational number. is not an integer. d. All multiples of 2 are even. 18 is a multiple of 3. 18 is even. 3. In the book, the Rule of Detachment and the Chain rule have accompanying truth tables. In these truth tables, they mark the rows which justify these two rules. Do the same for the Rule of Contrapositive.
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