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WEEK 4
Subject: Mathematics
TOPIC: Sets
- Definition of sets
- Set notations
- Types of sets
DEFINITION
A set is a general name for any group or collection of distinct elements. The elements of a set may be objects, names, points, lines, numbers or idea
The elements must have unique characteristics (specification) that can help to distinguish them from any other element outside the group or set. Hence, a set is a collection of well defined objects e.g.
- a set of mathematics text books
- a set of cutleries
- a set of drawing materials etc.
Sometimes there may be no obvious connection between the members of a set. Example: {chair, 3, car, orange, book, boy, stone}.
Each item in a given set are normally referred to as member or element of the set.
SET NOTATION
This is a way of representing a set using any of the following.
- Listing method
- Rule method or word description
- Set builders notation.
Listing Method
A set is usually denoted by capital letters and the elements in it can be defined either by making a list of its members. Eg A = {2, 3, 5, 7}, B = {a, b, c, d, e, f, g, h, i} etc.
Note that the elements of a set are normally separated by commas and enclosed in curly brackets or braces
Rule Method. The elements in a set can be defined also by describing the rule or property that connects its members. Eg C = {even number between 7 and 15. D= {set of numbers divisible by 5 between 1 and 52.}, B = {x : x is the factors of 24}etc
(iii) Set–Builders Notations
A set can also be specified using the set – builder notation. Set – builder notation is an algebraic way of representing sets using a mixture of word, letters , numbers and inequality symbols e.g. B = {x : 6 ≤ x < 11, x є ƶ} or B = {x/6 ≤ x < 11, x є I}. The expression above is interpreted as “B is a set of values x such that 6 is less than or equal to x and x is less than 11, where x is an integer (z)”
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