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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 furry

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 my hat

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 Jabberwocky from Through the Looking-Glass and What Alice Found There, 1872

Twas brillig, and the slithy toves
Did gyre and gimble in the wabe.

This question is based on an exercise from A Mathematical Bridge (2nd ed), by Stephen Hewson. Published by World Scientific.