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# Solutionx sx what is this equivalent to solutionx sx

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Unformatted text preview: But if P(x) is the statement “x &lt; 2”, then  both ∃x P(x)   and              ∀ x P(x) are false.   1.  Precedence of Quan*ﬁers    The quantiﬁers ∀ and  ∃ have higher precedence than  all the logical operators.    For example, ∀x P(x) ∨ Q(x) means (∀x P(x))∨ Q(x)      ∀x (P(x) ∨ Q(x)) means something different.   Unfortunately, often people write ∀x P(x) ∨ Q(x) when they mean ∀ x (P(x) ∨ Q(x)).   Transla*ng from English to Logic  Example 1:  Translate the following sentence into predicate  logic: “Every student in this class has taken a course in  Java.”  Solution:    First decide on the domain U.   Solution 1: If U is all students in this class, deﬁne a  propositional function J(x) denoting “x has taken a course in  Java” and translate as ∀x J(x). Solution 2: But if U is all people, also deﬁne a propositional   function S(x) denoting “x is a student in this class” and  translate as     ∀x (S(x)→ J(x)). ∀x (S(x) ∧ J(x)) is not correct. What does it mean? Transla*ng from English to Logic  Example 2: Translate the following sentence into  predicate logic: “Some student in this class has taken  a course in Java.”   Solution:  First decide on the domain U.   Solution 1: If U is all students in this class, translate as   ∃x J(x) Solution 1: But if U is all people, then translate as                  ∃x (S(x) ∧ J(x)) ∃x (S(x)→ J(x)) is not correct. What does it mean?  Returning to the Socrates Example     Introduce the  propositional functions Man(x)  denoting “x is a man” and  Mortal(x) denotin...
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## This document was uploaded on 03/06/2014 for the course MATH 320 at CSU Northridge.

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