¶ … 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 }

c) the odds of getting one head and one tail are two in four. Although Set B. only has three elements, the 1H1T element could arise from two different scenarios, head first and tail second or tail first and head second. This gives the odds of its occurrence as 2 in 4.

5 a) There are 11 possible sum outcomes if two six-sided dice are thrown. The set is { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

b) There are five possible combinations that could yield a 6, out of 36 potential combinations total. Therefore the odds of receiving a 6 are 5 in 36.

c) There are six possible combinations that could add up to a 7, out of 36 potential combinations. Therefore the odds of receiving a 7 are 6 in 36, or 1 in 6.