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→Functional quantifiers: + link
===Functional quantifiers===
===Functional quantifiers===
'''Exercise.''' Express the following in functional terms:
'''Exercises.''' Express the following in functional terms:
====<math>1. (\forall x \in X)(Px \Rightarrow Qx)</math>====
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:
* [[Directory:Jon_Awbrey/Papers/Functional_Logic_:_Quantification_Theory#Application_of_Higher_Order_Propositions_to_Quantification_Theory|Application of Higher Order Propositions to Quantification Theory]]
====<math>2. (\forall x \in X)(Px \Rightarrow Qx) \lor (Qx \Rightarrow Px)</math>====
====<math>3. (\forall x \in X)(Px \Rightarrow Qx) \lor (\forall x \in X)(Qx \Rightarrow Px)</math>====