How to Denote a Set?
You can denote a set by capital letters of English alphabets like A, B, C, …, Z, and its members are separated by commas and written within the brackets.
You can use the Greek letter ‘∈’ to represent that any object is “an element” of a set and ∉ to represent that an object is “not an element” of a set.
For Example
Set of Family members:
M = ｛Father, Mother, Brother, Sister｝
Now, you can represent elements of set M as:
Father ∈ M
And, you can read as Father belongs to set of family members M.
Grand Father ∉ M
Here Grand Father does not belong to a set of family members M.
Important Sets to remember:
Set of Natural Numbers
N = {1, 2, 3,...}
Set of Even Numbers
E = {0, 2, 4, 6,...}
Set of Odd Numbers
O = { 1, 3, 5,...}
Set of Whole Numbers
W = {0, 1, 2, 3,...}
Set of Prime Numbers
P = {2, 3, 5, 7, 11,...}
Set of Integers
Z = {0, ±1, ±2, ±3, ±4,...}
Example 1:
Identify that which of the following statements are true or false.
A = {5, 6, 7, 8} and B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(i) 9 ∈ A (ii) 8 ∈ B (iii) 3 ∉ A
(iv) 6 ∉ B (v) 7 ∈ A (vi) 1 ∈ B
Solution:
(i) 9 ∈ A
It is false because 9 is not an element of A.
(ii) 8 ∈ B
It is true because 8 is an element of B.
(iii) 3 ∉ A
It is true because 3 is not an element of A.
(iv) 6 ∉ B
It is false because 6 is an element of B.
(v) 7 ∈ A
It is true because 7 is an element of A.
(vi) 1 ∈ B
It is true because 1 is an element of B.
You can also practice the following exercises.
Exercise
Question#1:
Put symbols ∈ or ∉ in the following blanks:
(i) a .......... { b, c, d}
(ii) 2......... set of pets.
(iii) w......... {a, b, c,...., z}
(iv) b......... The set of capital letters of English Alphabets.
(v) cow........... The set of birds.
(vi) 14........... The set of counting numbers.
(vii) friends............ The set of family members.
(viii) 7............. The set of prime numbers.
(ix) Friday ............ The set of months names.
(x) Quetta ............ The set of cities of Pakistan.
Question#2
Represent the following into symbolic form.
(i) 0 is an element of set Z.
(ii) Lahore is an element of set C.
(iii) 1 is not a member of the set P.
(iv) Sindh is not an element of set B.
(v) Potato does not belong to the set W.
(vi) 3 is not an element of set E.
(vii) 9 is an element of the set W.
(viii) u is not an element of set A.
(ix) 5 is an element of the set O.
(x) f is not an element of the set F.
Question#3
List the elements of the following sets
(i) The set of five rivers of Punjab.
(ii) The set of three geometrical instruments.
(iii) The set of the first five prime numbers.
(iv) The set of seven days in a week.
(v) The set of three letters of alphabets.
(vi) The set of the first two Islamic months.
(vii) The set of three vegetable names.
(viii) The set of four fruits name.
(ix) The set of the three cities of Punjab.
(x) The set of twelve Islamic months.