Mathematical Logic

Hints for Chapters 5–9 Hints for Chapter 5.

5.1. Try to disassemble each string using Definition 5.2. Note that some might be valid terms of more than one of the given languages.

5.2. This is similar to Problem 1.5.

5.3. This is similar to Proposition 1.7.

5.4. Try to disassemble each string using Definitions 5.2 and 5.3.

Note that some might be valid formulas of more than one of the given languages.

5.5. This is just like Problem 1.2.

5.6. This is similar to Problem 1.5. You may wish to use your solution to Problem 5.2.

5.7. This is similar to Proposition 1.7.

5.8. You might want to rephrase some of the given statements to make them easier to formalize.

(1) Look up associativity if you need to.

(2) “There is an object such that every object is not in it.”

(3) This should be easy.

(4) Ditto.

(5) “Any two things must be the same thing.”

5.9. If necessary, don’t hesitate to look up the definitions of the given structures.

(1) Read the discussion at the beginning of the chapter.

(2) You really need only one non-logical symbol.

(3) There are two sorts of objects in a vector space, the vectors themselves and the scalars of the field, which you need to be able to tell apart.

5.10. Use Definition 5.3 in the same way that Definition 1.2 was used in Definition 1.3.

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