4.6: Exercises

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1. Consider the set of whole numbers from 1 to 10, inclusive. List the numbers that meet the condition: less than seven or odd

2. An accountant needs to withhold 13% of income for taxes if the income is below $40,000, and 20% of income if the income is $40,000 or more. The income amount is in cell A1. Write a spreadsheet expression that would calculate the amount to withhold.

3. Complete the truth table for the statement ~��⋀~��.

4. Complete the truth table for the statement ~�� → ��.

5. For the statement �� → ��, identify the inverse, converse, contrapositive, and original statement.

______ ~Q → ~R A. Inverse

______ ~R → ~Q B. Contrapositive

______ R → Q C. Converse

______ Q → R D. Statement

6. Complete the truth table for the statement (A ∨ B) ∧ C.

7. Complete the truth table for the statement ~(A ∨ B) ∧ C.

8. Complete the truth table for the implication ~(A ∧ B) → C.

9. Determine if the conclusion follows logically from the premises. Is this a valid or invalid argument?

Premise: No loving persons are thoughtless persons.

Premise: No loving persons are aggressive people.

Conclusion: No aggressive people are thoughtless persons.

10. Determine if the conclusion follows logically from the premises. Is this a valid or invalid argument?

Premise: All sensations are ideas of external material things.

Premise: Some ideas are not sensations.

Conclusion: Some ideas are not ideas of external material things.

11. Determine if the conclusion follows logically from the premises. Is this a valid or invalid argument?

Premise: All complex ideas are works of the mind.

Premise: All relations are works of the mind.

Conclusion: All relations are complex ideas.

12. Determine if the conclusion follows logically from the premises. Is this a valid or invalid argument?

Premise: If an animal is a rodent, then it is a mammal.

Premise: Rats are rodents.

Conclusion: Rats are mammals.

13. Determine if the conclusion follows logically from the premises. Is this a valid or invalid argument?

Premise: If it has an engine, I can fix it.

Premise: Cars have engines.

Conclusion: I can fix cars.

14. Determine if the conclusion follows logically from the premises. Is this a valid or invalid argument?

Premise: If I upgrade my computer, then it will run faster.

Premise: If my computer runs after, I will be more productive.

Conclusion: If I upgrade my computer, then I will be more productive.

15. Categorize the following logical fallacy.

“It was his fault, Officer. You can tell by the kind of car I'm driving and by my clothes that I am a good citizen and would not lie. Look at the rattletrap he is driving, and look at how he is dressed. You can't believe anything that a dirty, long-haired hippie like that might tell you. Search his car; he probably has pot in it.”

16. Categorize the following logical fallacy.

My client is an integral part of this community. If he is sent to prison not only will this city suffer but also, he will be most missed by his family. You surely cannot find it in your hearts to reach any other verdict than "not guilty."

17. Categorize the following logical fallacy.

“Old man Brown claims that he saw a flying saucer in his farm, but he never got beyond the fourth grade in school and can hardly read or write. He is completely ignorant of what scientists have written on the subject, so his report cannot possibly be true.”