“Practice in Logic” and “Extra Logic Homework 1”.

This homework is not required; it is just for those of you for whom logic is new, to give you some extra practice. Answers are provided. So try the problems, look at the answers to check yourself, and if you have remaining questions, ask me. The two sets are quite similar.

1. Practice in 1^st-Order Predicate Logic

4. Everyone loves himself.

5. Everyone loves everyone.

10. Every student walks or talks.

11. Every student who walks talks.

Extra Logic Homework #1. (not to hand in)

Use the notation and the predicates and constants given in the handout in which we did the syntax and semantics of predicate logic (Lecture 1). Add additional constants as needed. Translate the following English sentences into first-order predicate calculus. If any of the English sentences are ambiguous with respect to their ‘logical structure’, give two different translations that capture their two interpretations. (You are free to assume that D is a domain of humans, so that quantifier expressions like “No one”, “everyone”, etc., can be represented without the need for an additional predicate person.)

Feel free to send me notes, comments, and questions. There is not always a single right answer, and the meanings of the English sentences are not always clear-cut, e.g. when to interpret “if” as “if and only if”. If, after checking the answer sheet, you have questions about the interpretation of the sentence, or about whether what you wrote in your formula corresponds to how you in fact interpreted the sentence, ask me.

5. Someone loves everyone. (Ambiguous)

6. Someone walks and talks.

11. If anyone cheats, he suffers.

12. If anyone cheats, everyone suffers.