It is often the case that we want to prove statements that assert something is true for every element of a set. For example, “Every number has an additive inverse.” A statement that begins with the En...It is often the case that we want to prove statements that assert something is true for every element of a set. For example, “Every number has an additive inverse.” A statement that begins with the English words “every” or “all” is called universally quantified. It is asserted that the statement holds for everything within some universe. Statements that say something about a few (or even just one) of the elements of our universe are called existentially quantified.