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02-pred_logic - CSIS1118 Foundations of Computer Science...

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CSIS1118 Foundations of Computer Science Predicate Logic Hubert Chan ([O1,O2]; chapters 1.3, 1.4) 1
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Subjects and Predicates Do you still remember the definition of propositions? Is “x > 3” a proposition? N l th l f i fi d No, unless the value of x is fixed. Let P(x) denote the statement “x > 3” where P(x) is called a propositional function . P(x) has a truth value once the value of x is fixed. E.g. P(5) is true; P(1) is false. P actually refers to the property “is greater than 3” and is called the predicate . Note that x is a variable (the subject). A propositional function can have more than one variable (multi- value predicates). E.g. Let Q(x, y) denote “x + y > 10”. 2 Then, Q(4, 5) is false; Q(5, 6) is true.
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