Unformatted text preview: class who has not taken Java.” Symbolically ¬∀x J(x) and ∃x ¬J(x) are equivalent Nega$ng Quan$ﬁed Expressions ༉ Now Consider ∃ x J(x) “There is a student in your class who has taken a course in Java.” Here J(x) is “x has taken a course in Java” and the domain is students in your class. ༉ Negating the original statement gives “It is not the case that there is a student in your class who has taken Java.” ༉ This implies that “Every student in your class has not taken Java” Symbolically ¬∃ x J(x) and ∀ x ¬J(x) are equivalent De Morgan’s Laws for Quan$ﬁers ༉ The rules for negating quantiﬁers are: ༉ The reasoning in the table shows that: Transla$on from English to Logic Examples: 1. “Some student in this class has visited Mexico.” Solution: Let M(x) denote “x has visited Mexico” and S(x) denote “x is a student in this class” and domain be all people. ∃x (S(x) ∧ M(x)) 2. “Every student in this class has visited Canada or Mexico.” Solution: Add C(x) denoting “x has visited Canada.” ∀x (S(x) → (M(x) ∨ C(x))) Some Fun with Transla$ng from English into Logical Expressions ༉ U = {ﬂeegles, snurds, thingamabobs} F(x): x is a ﬂeegle S(x): x is a snurd T(x): x is a thingamabob Translate “Everything is a ﬂeegle” Solution: ∀x F(x) Transla$on (cont) ༉ U = {ﬂeegles, snurds, thingamabobs} F(x): x is a ﬂeegle S(x): x is a snurd T(x): x is a thingamabob “Nothing...
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This document was uploaded on 02/27/2014 for the course CS 215 at SIU Carbondale.
 Spring '14
 M.Nojoumian
 Computer Science

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