What does the negation of a statement represent?

The negation of a statement represents the opposite of the statement. In logical terms, if you have a true statement, its negation will be false, and if you have a false statement, its negation will be true. This concept is fundamental in logic and mathematics, as it allows for the exploration of opposite conditions or scenarios.

For example, if the original statement is "It is raining," the negation would be "It is not raining." Here, the negation directly contradicts the original statement by asserting its opposite. This is essential in logical reasoning, as it helps clarify arguments and assess truth values in various statements. Understanding negation is a key component of forming logical conclusions and validating hypotheses in mathematics and related fields.