Elements of a Set

A set can be defined as a group or a collection of well-defined objects, numbers or alphabets e.g. collection of books, shoes, cooking utensils, alphabets, clothes. A set is denoted by capital letters such as A, B, C, etc. while small letters are used to denote the elements e.g a, b, c, etc.

Elements of a Set: These are the elements or members of a given set. The elements are separated by commas and enclosed by a curly bracket {}.

e.g P = {1,2,3,4,5}, 3 is an element of P.

Example: List the elements in each of the following sets

P = {Even numbers from 1 to 10}

B = {Odd numbers from 10 to 20}

Solution

P = {2, 4, 6, 8, 20}

B = {11, 13, 15, 17, 19}
Cardinality of a Set

This is the number of elements in a set. In order words, it is the measure of the number of elements in the cell.

Examples:

Given that A = {all the months of the year}, B = {all the months of the year that begins with letter J}

(i)List all the elements of A., (ii) List the members of B, (iii)What is n(A)?, (iv) What is n(A) x n(B)?

Solution

(i) A = {January, February, March, April, May, June, July, August, September, October, November, December}

(ii) B = {January, June, July}, (iii) n(A) = 12, (iv) n(A) x n(B) = 12 x 3 = 36

Set Notation

Sets can be denoted algebraically using inequalities and other symbols. E.g. A = {x: -6 ≤ x ≤ 2, x is an integer}

Example: Highlight the members of the following sets