1. This is a puzzle about an island in which everyone is ...

[Pages:98]1. This is a puzzle about an island in which everyone is either a knight or a knave. Knights always tell the truth and knaves always lie. This problem is about two people A and B, each of whom is either a knight or a knave. A made the following statement:

At least one of us is a knave.

What are A and B?

(a) A and B are both knights. (b) A is a knight and B is a knave. (c) A is a knave and B is a knight. (d) A and B are both knaves. (e) None of the above.

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2. Let p and q be the propositions: p: It is below freezing. q: It is snowing. Which of the following expresses the statement:

It is either snowing or below freezing.

(a) p q (b) p q (c) p q (d) None of the above

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3. Let p and q be the propositions: p: It is below freezing. q: It is snowing. Which of the following expresses the statement:

It is snowing but not below freezing.

(a) p ?q (b) q ?p. (c) p ?q. (d) p q (e) None of the above (it is impossible to be above freezing

and snowing).

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4. On the island of knights and knaves, suppose A says, "Either I am a knave or B is a knight." What are A and B? (a) A and B are both knights. (b) A is a knight and B is a knave. (c) A is a knave and B is a knight. (d) A and B are both knaves. (e) None of the above.

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5. Determine whether the following statement is true or false: If 1 + 1 = 3 then 2 + 2 = 4.

(a) True (b) False (c) Part of it is true and part of it is false. (d) Can't decide, since the statement is nonsense.

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6. Choose the statement that describes you best. (a) I looked at the course website and the textbook. (b) I looked at the course website but not the textbook. (c) I looked at the textbook but not the course website. (d) I haven't looked at either, but I will before next class.

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7. What is my name? (a) Dr. Ford (b) Dr. Doedel (c) Dr. Narayanan (d) Don't know

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8. p q (p ?q) (?p q) (a) is a true statement. (b) is a false statement. (c) is sometimes true, sometimes false. (d) don't know.

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