Eng ek 381 ~ fall semester ~ prof. goyal. Foundation of probability: a number of specific definitions of terms, axioms, brief review of the set theory, a set is a collection of elements where the elements can be anything a. i. A is a proper subset of b" means that there exist elements elements which are found in b but not in a. In a sense, b cannot be a subset a subset of a. A and b are called disjoint when anb = Note: disjoint are mainly applied to 2 sets while mutually exclusive applied to more than 2 sets. Sanity check: a and a can be disjoint only when a = . A non- empty set cannot be disjoint with itself. Several sets are called collectively exhaustive when the union of the sets is equal to the universal set.