COSI 29A Chapter 1.3: Predicates and Quantifiers
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Department
Computer Science
Course
COSI 29A
Professor
Cherniack Mitch
Semester
Fall

Description
Chapter 1.3 Outline Predicates and Quantifiers Pages 28 – 44 Quantifiers The predicate refers to a property that the subject can have. For example, in 𝓍 > 3 the subject is 𝓍 and the predicate is > 3. Ex: P(𝓍) = 𝓍 > 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(𝓍) is true for all values of 𝓍 in the domain, aka universe of discourse. Ex: Let P(𝓍) be 𝓍 + 1 > 𝓍. What is the truth value of the quantification βˆ€π“π‘ƒ(𝓍), where the domain is all real numbers? Note that βˆ€ is the universal quantifier, so the quantification βˆ€π“π‘ƒ(𝓍) means for all 𝓍𝑃(𝓍). Since 𝓍 + 1 > 𝓍 is true for all real numbers 𝓍, the quantification βˆ€π“π‘ƒ(𝓍) is true. Ex: Let P(𝓍) be 𝓍 < 2. What is the truth value of βˆ€π“π‘ƒ(𝓍)? Since 𝓍 < 2 is not true for the value 𝓍 = 3, 𝓍 < 2 is not true for all real numbers 𝓍, the quantification βˆ€π“π‘ƒ(𝓍) is false. The existential quantification means that P(𝓍) is true if there is an 𝓍 that is true. Ex: Let P(𝓍) be 𝓍 > 3. What is the truth value of the quantification βˆƒπ“π‘ƒ(𝓍), where the domain is all r
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