Language, Logic and Information

Exercise 3

(Propositional Logic)

Date handed out: 31 October, 2006

Date due: 6th November, 2006, 12:00 noon

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1. For each of the following sentences, answer whether it has a propositional conjunction. If it does, you would want to think about what the two component sentences are.

a. Susan got married and had a child

b. John and Marry got married to each other on Tuesday.

c. Jane speaks both French and English.

d. Jane is bilingual because she speaks both French and English.

e. Fred had pie and ice cream for dissert.

Answers: ______

2. For each of the following sentences mention whether it is a direct negation of another sentence, i.e., whether it is of the form . If it is, state what the sentence P is.

a. There is not enough work in this module.

b. It is not going to rain tomorrow.

c. Kirstin is not smart or rich.

d. I may not have answered this correctly.

e. Sometimes I do not feel like working.

Answers: ______

3. Which of the following arguments are valid by virtue of their propositional form?

a. Donald owns a tower in New York and a palace in Atlantic City. Therefore, Donald owns a palace in Atlantic City.

b. Tom owns a house. Therefore, Tom owns a house and a piece of land.

c. Sandy can do either BSc Computer Science or BEng Software Engineering. Sandy is doing BSc Computer Science. Therefore, she is not doing BEng Software Engineering.

d. Mary goes to class whether it rains or not. Therefore, Mary goes to class.

e. John will play only if the situation is hopeless. The situation is hopeless. So, John will play.

Answers: ______

4. Using the truth table techniques, test the following arguments for validity. Indicate which of them are valid argument forms.

Answers: ______