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# Teacheschanx producestheresponse x kevin x kiko no

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Unformatted text preview:  a student in your class who  has not taken calculus.”  Symbolically ¬∀x J(x) and ∃x ¬J(x) are equivalent Nega*ng Quan*ﬁed Expressions  (con#nued)    Now Consider ∃ x J(x)  “There is a student in this class who has taken a course in  Java.” Where J(x)  is “x has taken a course in Java.”    Negating the original statement gives “It is not the  case that there is a student in this class who has taken  Java.” This implies that “Every student in this 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:    These are important. You will use these.   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 U 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...
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## This document was uploaded on 03/06/2014 for the course MATH 320 at CSU Northridge.

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