Questions on Set Theory, Essay Example

Short Definition Of The Following

A set is a collection of related objects with mathematical sense. The composition of a set qualifies owing to the mathematical characteristics of the objects contained therein. The characteristics of sets denote that, if the components of set A are members of set B, then set A is subset of set B. This is denoted as AB and is pronounced as A contained in B.

A proper subsets are those that are contained in another set and excludes at least one number of the set. For example A is a proper subset of B if set A(6,7,8) and B(4,5,6,7,8,9). It is denoted as AB.

The compliment of a set is all the components of the universal set (U) absent in set A. As a result, it is denoted A^C and can be expressed as n (A) +n (A^C) =n (U). On the other hand, the intersection of two sets refers to the common characters in the sets A and B. as a result, the intersection of sets is that character which is duplicated in two or more sets. For example, the intersection of sets A(6,7,8,9) and B(1,2,3,4,5,6,7) is 6 and 7 since these two appear in sets A and B.

Union of a sets, depicted by A  B (A union B), denotes the elements present in A or B or both sets. For example, assuming that the universal set U ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, set A= {2, 4, 5} and set B ={1, 2, 3, 4, 5, 6, 7}, the union of set A and B is {1,2,3,4,5,6,7}

Provide an answer to the following problems:

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

The union of set X and Y is X Y= {5, 7, 11, 16, 19, 21, 702}

Intersection of set X and Y is 5, 11 and 702

Z a subset of X would appear like Z= {5,7,11}

Let Set 1 be the entire alphabet. Let Set 2 = {g, h, i, j, k, l}.

The complement of set 2 in set 1 is the rest of the alphabet that do not appear in the set 2. That is {a, b, c, d, e, f, m, n, o, p, q, r, s, t, u, v, w, x, y, z}

Set 3 = {h, i, j, k}is  a proper subset of set 2 = {g, h, i, j, k, l} since all the character in set three are present in set two, although set two contains elements which are not present in set 3.

Take out a coin for the following problems:

Suppose you are going to flip a coin once. What is the set of possible outcomes for this?

Assume H denotes heads while T denotes tails, the set outcome, R, after one flip is R= {H, T}. After flipping it twice, the set outcome S= {H, T, H, T}. The possibility that you will get one head and one tail is one in two.

Consider two identical six sided dice with from one to six dots on each side with no two sides containing the same number of dots.

The possible outcomes of the dice toss are tabulated as follows.

The possible outcomes as shown above are {2,3,4,5,6,7,8,9,10,11,12}, thus total is 11 outcomes.

Since the possibility that the outcome of six is 5 among the 36 outcomes, the possibility that the sum is 5 out of 36 times.

The possibility that the outcome of the dice rolled will sum up to 7 is 6 out of 36.