Set theory: definitions, operations, and probability applications

¶ … Theory

A set can be defined as a collection of distinct objects. A subset is a smaller set that lies at least partially within the larger set. Thus if Set a = { 1, 2, 3 } then a subset would be { 2, 3 }.

A proper subset is one that is entirely contained within the set. The above example has subset B. that is a proper subset of Set a.

The complement of a set is that which lies outside of the set. In the example above, the complement of Set B. In a would be { 1 }.

Unions are made when two or more sets are taken together and includes all things that are in all of the union sets combined. If Set a = {1, 2} and Set B = {2, 3} then the union of sets a and B. would be { 1, 2, 3}

The intersection is comprised of all things that are in both sets. In the example above, the intersection of sets a and B. would be { 2 }

X ? Y = { 2, 5, 7, 8, 11, 16, 19, 21, 702 }

b) X ? Y = { 5, 11, 702 }

c) Z = { 7, 11 }

a) 1 / 2 = { a, b, c, d, e, f, m, n, o, p, q, r, s, t, u, v, w, x, y, z }

b) Set 3 is a proper subset of Set 2. All of the elements in Set 3 are contained within Set 2.

4 a) { heads, tails }

b) { 2 heads, 1 head & 1 tail, 2 tails }