redefine set using the descriptive property B=(b /when c=2, a+3b =-7)
Answers
Describing and Defining Sets
Related Topics: More Lessons on Sets
This lesson is part of a series of lessons on sets.
In this lesson, we will learn
how to define sets and set notations
subsets and proper subsets
Venn diagrams and set operations
The following table shows some Set Theory Symbols. Scroll down the page for more examples and solutions of how to use the symbols.
Set Symbols
A set is a collection of objects, things or symbols which are clearly defined.
The individual objects in a set are called the members or elements of the set.
A set must be properly defined so that we can find out whether an object is a member of the set.
1. Listing the elements(Roster Method)
The set can be defined by listing all its elements, separated by commas and enclosed within braces. This is called the roster method.
Example:
B = {2, 4, 6, 8, 10}
X = {a, b, c, d, e}
However, in some instances, it may not be possible to list all the elements of a set. In such cases, we could define the set by method 2.
2. Describing the elements
The set can be defined, where possible, by describing the elements. This is called the set-builder notation.
Example:
C = {x : x is an integer, x > – 3 }
This is read as: “C is the set of elements x such that x is an integer greater than –3.”
D = {x: x is a river in a state}
We should describe a certain property which all the elements x, in a set, have in common so that we can know whether a particular thing belongs to the set.
We relate a member and a set using the symbol ∈. If an object x is an element of set A, we write x ∈ A. If an object z is not an element of set A, we write z ∉ A.
∈ denotes “is an element of’ or “is a member of” or “belongs to”
∉ denotes “is not an element of” or “is not a member of” or “does not belong to”
Example:
If A = {1, 3, 5} then 1 ∈ A and 2 ∉ A
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