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'Notty Logic' printed from http://nrich.maths.org/
The negation NOT$(P)$ of a statement is true if and only if the
statement $P$ is false. A well-constructed negation uses positive
language, avoiding the use of the word NOT.
Here are two statements, each
with four suggested negations. Which of these are the correct
negations and why?
1. A good pet is friendly and
A. A good pet is unfriendly and unfurry
B. A bad pet is friendly and furry
C. A good pet is unfriendly or unfurry
D. A bad pet is unfriendly or unfurry
2. That man is lying or I'll eat
A. That man is telling the truth and I won't eat my hat
B. Either that man is telling the truth or I won't eat my hat
C. I won't eat my hat or that man is telling the truth
D. That man is telling the truth and I don't have a hat
Have a go at negating this sentence:
If you don't go to the party and
if John goes to the party then I won't go to the party
Finally, try to negate this sentence taken from Lewis Carrol's
from Through the Looking-Glass and What
Alice Found There, 1872
Twas brillig, and the slithy
Did gyre and gimble in the
This question is based on an exercise
A Mathematical Bridge (2nd ed), by
Stephen Hewson. Published by World Scientific.