Negation of Quantified Statements


Question Formal Representation Negations
1. All dogs bark. dogs d, d barks
~( dogs d, d barks)
dogs d, ~(d barks)
dogs d, d does not bark
Some dogs do not bark.
2. Most cars are inexpensive. cars c, c is inexpensive ~(cars c, c is inexpensive)
cars c, ~(c is inexpensive)
cars c, c is not inexpensive
No car is inexpensive.
3 Every day I bring lunch to work. days, I bring lunch to work ~(days, I bring lunch to work)
days, ~(I bring lunch to work)
days, I do not bring lunch to work
Some days I don't bring lunch to work.
4 Cheaters never prosper. cheaters c, c never prospers ~(cheaters c, c never prospers)
cheaters c, ~(c never prospers)
cheaters c, c prospers
Some cheaters prosper.
5. Some people are born lucky. people p, p is born lucky ~(people p, p is born lucky)
people p, ~(p is born lucky)
people p, p is not born lucky
No one is born lucky.