Answer to Question #190956 in Discrete Mathematics for Maaz

Question #190956

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


1
Expert's answer
2021-05-10T14:05:17-0400

Solution:

a. "\\forall x" ( Likes (x, mathematics ) . Its negation:"\\exists" x("\\neg" Likes(x, mathematics )). i.e., Some student in this class do not like mathematics.

b. "\\exists" x( Notseen (x, computer )) . Negation: "\\forall x" "\\neg"( Notseen (x, computer )). i.e., Every student in this class has seen a computer.

c. "\\exists" x "\\forall y"(taken(x, y)). Negation: "\\forall x" "\\exists" y "\\neg"(taken(x, y)). i.e., Every student in this class has not taken a mathematics course offered at this school.

d. "\\exists" x "\\forall y" "\\exists" z( within (z, y) "\\wedge" attended (x, z)). Negation: "\\forall x" "\\exists" y "\\forall z" "\\neg"( within (z, y) "\\wedge" attended (x, z)). i.e., Every students in this class has not been in all the rooms of a building on campus.


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