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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen
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Express the negations of these propositions using

Chapter 7, Problem 38E

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QUESTION:

Express the negations of these propositions using quantifiers, and in English.a) Every student in this class likes mathematics.________________b) There is a student in this class who has never seen a computer.________________c) There is a student in this class who has taken every mathematics course offered at this school________________d) There is a student in this class who has been in at least one room of every building on campus.

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QUESTION:

Express the negations of these propositions using quantifiers, and in English.a) Every student in this class likes mathematics.________________b) There is a student in this class who has never seen a computer.________________c) There is a student in this class who has taken every mathematics course offered at this school________________d) There is a student in this class who has been in at least one room of every building on campus.

ANSWER:

Solution:Step-1: In this problem we need to express the negations of the given propositions using quantifiers , and in english. Quantifiers : Universal Quantifier - for all elements. Existential Quantifier - there exist an element.Step-2: a)Given : Every student in this class likes mathematics. Let us consider , S(x) - x is a student in the class and D (x , y) represents x likes y . Every student in this class likes mathematics means . Negation of the given statement by using quantifiers : No one in this class likes mathematics means . In simple english : means No one in this class likes mathematics that means some student in class that does not like mathematics.Step-3 :b) Given : There is a student in this class who has never seen a computer.Let us consider , S(x) - x is a student

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