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Unformatted text preview: ECS20 Handout 2 January 6, 2011 Propositional function – predicate and quantifier 1. Propositional function P ( x ): a statement involving the variables x Examples • Let P ( x ) denote “ x > 3”, what are the truth values of P (4) and P (2)? • Let Q ( x,y ) denote “ x = y + 3”, what are the truth values of the proposition Q (1 , 2) and Q (3 , 0)? 2. A statement of the form P ( x 1 ,x 2 ,...,x n ) is the value of the propositional function P at the n-tuple ( x 1 ,x 2 ,...,x n ), and P is called the predicate . 3. The domain of discourse , denoted as U , is the set of values x that x is allowed to take in P ( x ). 4. The universal quantification of P ( x ) is the proposition “ P ( x ) is true for all value of x in U ”. Notation: ∀ x P ( x ), ∀ is called the universal quantifier. Truth values of ∀ xP ( x ) “ ∀ xP ( x )” = True, when P ( x ) is true for every x in U ....
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This note was uploaded on 05/31/2011 for the course ECS 20 taught by Professor Staff during the Winter '08 term at UC Davis.
- Winter '08