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Tomlee2060 (talk | contribs) m minor English |
Quantifiers have the highest precdence among logical operators: see page 12 of http://www.cs.laurentian.ca/jdompierre/MATH1056E_F2008/cours/s1.3_predicates_quantifiers.pdf |
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Line 17:
:''For every mouse m, there exists a cat c, such that c is feared by m,''
:<math>\forall m. \, (\, \text{Mouse}(m) \rightarrow \exists c. \, (\text{Cat}(c) \land \text{Fears}(m,c)) \, )</math>
in which case the conclusion is trivial.
Line 24:
:''There exists a cat c, such that for every mouse m, c is feared by m.''
:<math>\exists c. \, ( \, \text{Cat}(c) \land \forall m. \, (\text{Mouse}(m) \rightarrow \text{Fears}(m,c)) \, )</math>
This example illustrates the importance of specifying the scope of quantifiers as ''for all'' and ''there exists''.
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