MATH 1P66 Lecture Notes - Lecture 4: Existential Quantification, Propositional Function, First-Order Logic

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Predicates are propositions functions that are rather similar to algebraic functions. The predicate part of the propositional function refers to a property that the subject of the statement has. Not a proposition unless a value is assigned from the domain. " is greater than 3" domain = { } Once a value has been assigned to it can be treated as a. " is the parent of obama" domain = {people} Example: " can be represented as and are variables. In a statement if the number of variables is represented by would be known as an -place predicate or an -ary predicate. Statements can have as many parameters as you want. Statements can also have more than one variable. Quantification is a way in which a propositional function can be turned into a proposition without assigning its variables any values. Quantification expresses extent of the truth of a predicate over a range of elements (all, some, many, none etc. )

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