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
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.
Comments
Leave a comment