ABSTRACT
Mathematics has always been concerned with “provable truth.” The statements are unambiguous in their truth or falsehood. Surprisingly, however, only one of the statements is false. Just as one is able to use conjunctions and disjunctions to combine statements into new statements, one can combine sets into new sets. This chapter discusses what it means to take a statement’s “opposite,” which is called as the negation of a statement. The statements are either true or false, and therefore the negated statement will be a statement in its own right, and will have the opposite truth value of the original statement. Universal quantifiers are typically statements that claim all objects of a certain type will satisfy a certain property. When negating such statements, one really claims that not all objects of the specified type satisfy a certain property. In other words, one is claiming that there exists at least one object of that type that does not have the specified property.
