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COSI 29A (3)
Chapter 1.3

# COSI 29A Chapter 1.3: Predicates and Quantifiers Premium

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School
Department
Computer Science
Course
COSI 29A
Professor
Cherniack Mitch
Semester
Fall

Description
Chapter 1.3 Outline Predicates and Quantifiers Pages 28 ā 44 Quantifiers The predicate refers to a property that the subject can have. For example, in š > 3 the subject is š and the predicate is > 3. Ex: P(š) = š > 3 What are the truth values of P (4) and P (2)? P (4) is true. P (2) is false. The universal quantification means that P(š) is true for all values of š in the domain, aka universe of discourse. Ex: Let P(š) be š + 1 > š. What is the truth value of the quantification āšš(š), where the domain is all real numbers? Note that ā is the universal quantifier, so the quantification āšš(š) means for all šš(š). Since š + 1 > š is true for all real numbers š, the quantification āšš(š) is true. Ex: Let P(š) be š < 2. What is the truth value of āšš(š)? Since š < 2 is not true for the value š = 3, š < 2 is not true for all real numbers š, the quantification āšš(š) is false. The existential quantification means that P(š) is true if there is an š that is true. Ex: Let P(š) be š > 3. What is the truth value of the quantification āšš(š), where the domain is all r
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