Exercise-ch2: Difference between revisions
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== Formulae == | == Formulae == | ||
∀ ∃ ∧ ∨ ⊂ ⊃ ¬ | <!-- ∀ ∃ ∧ ∨ ⊂ ⊃ ¬ --> | ||
For the following exercises we use names and properties from the ''The Lord of the Rings'' novels. | For the following exercises we use names and properties from the ''The Lord of the Rings'' novels. | ||
| Line 15: | Line 15: | ||
+ '''gandalf''' | + '''gandalf''' | ||
+ '''hobbit''' | + '''hobbit''' | ||
- ∃ ''x'' | - ∃''x'' | ||
|| A quantifier, ∀ or ∃, can only be used with a variable and a formula. For example: ∃''x''('''hobbit'''(''x'')) | || A quantifier, ∀ or ∃, can only be used with a variable and a formula. For example: ∃''x''('''hobbit'''(''x'')) | ||
- '''know'''('''gandalf''') | - '''know'''('''gandalf''') | ||
| Line 28: | Line 28: | ||
- '''frodo''' ∧ '''gandalf''' | - '''frodo''' ∧ '''gandalf''' | ||
+ ∀''x'' ('''hobbit'''(''x'') ⊃ x = '''gandalf''') | + ∀''x'' ('''hobbit'''(''x'') ⊃ x = '''gandalf''') | ||
+ ∃''y''('''hobbit'''(''x'') ∨ '''wizard'''(''gandalf'')) | |||
|| Note: The variable bound by the quantifier, ''y'', need not occur in the scope of the quantifier. | |||
</quiz> | </quiz> | ||
Revision as of 19:44, 15 March 2013
Additional Exercises for Chapter 2: Predicate Logic
Formulae
For the following exercises we use names and properties from the The Lord of the Rings novels.
Names: frodo, sam, gandalf, aragorn
1-place predicates: hobbit
2-place predicates: know, help