Types of sets

This is a set that contains everything that we are interested in. The symbol for universal set is μ or U. For example, the set of Integers contains all the elements of sets such as odd numbers, prime numbers, even numbers, counting numbers and whole numbers. In this example the set of integers is the Universal set.

Another example of a Universal set is a Set of all English Alphabets which contains all elements of a set of vowels and set of Consonants.

Is a set with no elements. There aren't any elements in it. Not one. Zero elements. For example; A set of Countries South of the South Pole.

It is represented by Ø or {}.

Is a set which its elements can be counted. We can say how many members are there. For example; a set B is a set of numbers between 1 and 7. When we list the elements, then set B = {2,3,4,5,6}. So, there 5 elements. This set is called finite set.

This is a set whereby we cannot count the number of elements of the set. We cannot tell how many members are there in a set. For example; A is a set of all real numbers. Real numbers are all positive and negative numbers including fractions. We cannot count the members of a set of real numbers. Another example; B = {1,2,3,…}. Three dots means go on or infinite, we will go on with no end. This types of sets are called infinite sets.

Two sets are said to be equivalent if their members match exactly. For example; if A = {a, b, c, d} and B = {w, x, y, z} the two sets match like this:

Generally, two sets are equivalent if n(A) = n(B). Symbolically we write A ≡ B which means A is equivalent to B.

If two sets are equivalent and their members are alike, then the two sets are said to be equal. For example; if A = {a, b, c, d} and B = {c, a, b, d} then the two sets are equal since a is in set A and in set B, b is in set A and in set B, c is in set A and in set B and d is in set A and in B. Also, numbers of elements of the both sets are equal. Therefore A = B (set A is equal to set B)