Identify The Sets
A set is a collection of well-defined objects
A set is well-defined if we are able to tell whether or not any particular object is an element of the set
Example:
Which of the following are well-defined sets?
(1) All the tall girls of the school
(2) All the letters in the word "mathematics"
(3) All the hardworking teachers in a school
(4) All the honest members in the family
Answer: (2)
All the letters in the word "mathematics" is well-defined sets
B = {m, a, t, h, e, i, c, s}
The following conventions are used with sets:
- Capital letters are used to denote sets
- Curly braces { } denote a list of elements in a set
- Lowercase letters are used to denote elements of sets
Example:
A is the set of vowels
A = {a, i, u, e, o}
The elements in the sets are depicted in either the statement form, set-builder notation form or roster form
- Statement form
A = {prime numbers between 10 and 30}
- Set-builder notation
A = {x| 10 < x < 30, x ∈ prime numbers}
We read it as,
"A is the set of all x such that x is more than10 but less than 30 and x belongs to prime numbers"
- Roster form
A = {11, 13, 17, 19, 23, 29}