Final answer:
Trivial negation and nontrivial negation are terms used in logic to describe the negation of a statement. For example, the statement 'All cats have tails' is negated by 'Some cats do not have tails'.
Step-by-step explanation:
In mathematics, trivial negation and nontrivial negation are terms used in logic to describe the negation of a statement.
A trivial negation is when the negation of a statement is logically equivalent to the statement itself.
For example, the statement 'It is raining' is negated by 'It is not raining'.
A nontrivial negation, on the other hand, is when the negation of a statement is not logically equivalent to the statement.
For example, the statement 'All cats have tails' is negated by 'Some cats do not have tails'.