Lesson 1
Key unit competence
By the end of the unit, I should be able to use sets, venn diagrams and relations to represent situations and solve problems.
Unit outline
• Set concept.
• Relations.
• Inverse and composite relations.
1.1 Introduction to set concept
Activity 1.1
In groups of four:
1. Identify and list any ten items in your home that can be grouped together.
2. Name the groups you have identified in step 1 above.
3. Let the group members select one member to present their findings in part 1 and 2 on the chalk board.
From Activity 1.1 above, you may have obtained groups that consist of utensils, domestic animals, furniture and so on. Most things in life have common features. Such features are used to group the things together. A group of items with a common feature is called a set. Examples of sets are: a set of animals, a set of houses, set of cars and so on. An object or item in a set is called a member or an element of the set. This unit will introduce us to the knowledge of sets and a number of terms concerning sets. We will define the terms as we meet them in their respective sections.
1.2 Describing sets
Activity 1.2
In groups of three:
1. Find out from the internet, reference books or any other relevant materials how sets are described.
2. By use of examples, show other students how sets are described on the chalkboard. There are three methods commonly used to describe or represent a set
(i) Statement form method
(ii) Roster or tabular form method
(iii) Set builder form method All these methods are used together with a pair of curly brackets within which thedescription is enclosed.
(a) Statement form method
Consider:
(i) the alphabets a, b, c, d and e. These letters can be described using a statement as follows: {the first six
letters of the alphabets}
(ii) the set of the numbers 2, 4, 6, 8, 10.This can be described as: {the first five even numbers} or {the first five natural numbers divisible by 2} Individually, identify another five sets and describe them in a similar method.
(b) Roster or tabular method Using this method, we describe a set by listing all the elements in it.
For example, consider the set of all the letters in the word Mathematics. This set can be described by listing all the elements in it. If we let this set be N, then N = {m, a, t, h, e, i, c, s}
This method of describing sets is known as Roster or Tabular Method.Note that each element is written only once.For example in the word mathematics, the letters m, a and t, each appear twice but we list each of them only once.
3. Set builder form method In this method, we describe a set by using a rule or an algebraic formular which
defines only the set we want. For example, A = {x : 1 < x < 10} is read as the set ofintegers x such that x lies between 1 and 10. thus A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} when a set is described using an algebraic expression, we say we are using set builder notation. The symbol: in the statement {x : 1 < x <10, x ∈N}is used to denote the statement “such that”
