4: Predicate logic
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- 4.1: Predicates and Quantifers
- We often let variables represent arbitrary mathematical objects. However, as we have seen, object variables or free variables (as opposed to statement variables) lead to problems in logic.
- 4.2: Manipulating quantified statements
- Negating quantified statements in English can be tricky, but we will establish rules that make it easy in symbolic logic.
- 4.3: Vacuously true statements
- We have to be careful with quantified predicates because it is (seemingly) possible to violate the Law of Contradiction (see Basic Tautology 4 in Example 1.4.1).