Express the negation of these propositions using quantifiers, and then express the negation in English.a) Some drivers do not obey the speed limit.b) All Swedish movies are serious.c) No one can keep a secret.d) There is someone in this class who does not have a good attitude
Question
Express the negation of these propositions using quantifiers, and then express the negation in English.a) Some drivers do not obey the speed limit.b) All Swedish movies are serious.c) No one can keep a secret.d) There is someone in this class who does not have a good attitude
Solution
a) The negation of "Some drivers do not obey the speed limit" is "All drivers obey the speed limit". In terms of quantifiers, it can be expressed as "For all x, if x is a driver, then x obeys the speed limit".
b) The negation of "All Swedish movies are serious" is "There exists a Swedish movie that is not serious". In terms of quantifiers, it can be expressed as "There exists an x such that x is a Swedish movie and x is not serious".
c) The negation of "No one can keep a secret" is "There exists someone who can keep a secret". In terms of quantifiers, it can be expressed as "There exists an x such that x can keep a secret".
d) The negation of "There is someone in this class who does not have a good attitude" is "Everyone in this class has a good attitude". In terms of quantifiers, it can be expressed as "For all x, if x is in this class, then x has a good attitude".
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