Negation of Quantified Statements
Answers
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. |