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, 18:42, 8 December 2008
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| ===Functional quantifiers=== | | ===Functional quantifiers=== |
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− | '''Exercise.''' Express the following in functional terms: | + | '''Exercises.''' Express the following in functional terms: |
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− | * <math>(\forall x \in X)(Px \Rightarrow Qx)</math>
| + | ====<math>1. (\forall x \in X)(Px \Rightarrow Qx)</math>==== |
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− | This is the just form <math>\operatorname{All}\ P\ \operatorname{are}\ Q,</math> already covered here: | + | This is the just the form <math>\operatorname{All}\ P\ \operatorname{are}\ Q,</math> already covered here: |
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− | …
| + | * [[Directory:Jon_Awbrey/Papers/Functional_Logic_:_Quantification_Theory#Application_of_Higher_Order_Propositions_to_Quantification_Theory|Application of Higher Order Propositions to Quantification Theory]] |
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− | * <math>(\forall x \in X)(Px \Rightarrow Qx) \lor (Qx \Rightarrow Px)</math>
| + | ====<math>2. (\forall x \in X)(Px \Rightarrow Qx) \lor (Qx \Rightarrow Px)</math>==== |
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− | * <math>(\forall x \in X)(Px \Rightarrow Qx) \lor (\forall x \in X)(Qx \Rightarrow Px)</math>
| + | ====<math>3. (\forall x \in X)(Px \Rightarrow Qx) \lor (\forall x \in X)(Qx \Rightarrow Px)</math>==== |