The document introduces sets and provides examples and explanations of key set concepts. It is written by Aisha Kanwal Memon, a telecommunications engineer from Pakistan who works to help teachers prepare students for exams. The summary defines what a set is, provides examples of finite and infinite sets, and explains concepts like elements, subsets, equality of sets, and notation for sets. It also includes multiple choice questions about sets and examples of writing sets in tabular form.

1. Mathematics Brief &
MCQs – Grade VI
Chapter Number 1
Sets
Engr. Aisha Kanwal Memon

2. Who is Aisha Kanwal Memon?
› Living in city Hala, District Matiari, Sindh, Pakistan
› A telecommunication engineer from Quaid-e-Awam University
of Engineering, Science and Technology – QUEST,
Nawabshah
› Currently, doing Master of Engineering in Communication and
Computer Networks from QUEST, Nawabshah
› Joined Indus Education Foundation in February 2019 and
working as a Program Manager and running million-dollars
project in collaboration with Sindh Education Foundation, and
Sindh Doctor Association UK.
› Here with an aim to help secondary school teachers and
those candidates who are preparing for JEST and PST Jobs.

3. CHAPTER # 1 SETS – SUMMARY (1)
› Georg Cantor was first mathematician who gave the concept of set in 1870’s.
› A set is a collection of well defined and distinct objects. – A={1,2,a,b}, S={aisha, asquare}
› Each object in a set is an element or member of the set.
› The name of a set is denoted by capital letters of English alphabet. – A, B, C, …, X, Y, Z
› Elements of set do not repeat itself.
› A set is described in three ways.
– Descriptive form: Precisely described in words. – A is the set of first five natural numbers
– Tabular form: All the elements are listed down separately. – A = {1,2,3,4,5}
– Set Builder form: stating the properties that members of set satisfies. – A = {x|x ᕮ N ⋀ x < 6 }
› Finite set has limited number of elements – X= {1,2,3,4,5} or Z={1,2,3,…..,100}
› Infinite set has unlimited number of elements. – Y = {1,2,3,4,5,6,…….}
› A set having no element is an Empty or Null set or void set. – { }, Ø(phi)
› A set having only one element is called Singleton set. – {{}}, {Ø}, {0}, {asquare}

4. CHAPTER # 1 SETS – SUMMARY (2)
› Two sets are equal if they have all same elements.
› Example of equal sets: A={1,2}, B={1,2} then A = B.
› Two sets are equivalent if they have same number of elements.
› Example of equivalent sets: A={1,2}, B={a,b} then A ~ B.
› Every set is a subset of itself.
› B is a subset of A, if every element of B is also an element of A.
› Proper subset: if set A is subset of set B, and A is not equal to B then A is
proper subset of set B. then symbolically, we write as A⊂B
› Example of proper subset: A={1} and B={1,2,3}
› Improper subset: if set A is subset of set B and A is also equal to B then A
is called improper subset of set B. symbolically, we write as A⊆B
› Example of proper subset: A={1,2,3,4} and B={4,2,1,3}

5. SYMBOLS TO REMEMBER
Let suppose if A={1,2,3} and B={1,2}
Then
If C={1,2,3} and D={a,b,c}
Then
2 ∈ A 3 ∉ B
A = C and C ~ D
A ≠ B and A ≠ D
A ⊆ C, B ⊂ A, B ⊂ C
A ⊇ B, D⊈A

6. Multiple Choice Questions - MCQs

7. MCQ # 1
Concept of a set is given by ________________
mathematicians.
a. Newton
b. Albert Einstein
c. Galileo Galilei
d. George Cantor

8. MCQ # 2
If B is set of first five consonants of English Alphabet;
choose the correct option.
a. p Є B
b. b Є B
c. b B
d. e Є B
∉

9. MCQ # 3
A = {{}}, then A is called a ___________ set.
a. Null
b. Empty
c. Singleton
d. Bracket

10. MCQ # 4
A={1,2,3} and B={2,3,4} then set A and B are said to be:
a. Equal sets
b. Equivalent sets
c. Subsets
d. Supersets

11. MCQ # 5
A={a,b,c} and B={a,b,c,d} then which statement is correct?
a. Set A is equal to set B
b. Set A equivalent to set B
c. Set A is superset of set B
d. Set A is a subset of set B

12. MCQ # 6
If A={2,4} and B={2,4} then which statement is incorrect?
a. A ⊆ B
b. A = B
c. A ~ B
d. A Є B

13. Do It Yourself - DIY

14. Write the following sets in tabular form.
i. A is set of all even numbers between 2 and 10.
ii. B is set of all off numbers from 1 to 17
iii. C is set of natural numbers divisible by 2 and less than 30.
iv. D is set of months of a solar calendar beginning with letter “J”.
Solve the followings!

15. Which of these sets are finite and which of these are infinite?
i. A is set of members of your family
ii. B is set of stars in the sky.
iii. C is set of prime factors of 60.
iv. D is set of one-digit natural numbers
Solve the followings!

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