as per instruction here is the assignment 1 having min. 12 slides with welcome and thanks for the emrolled fdp by Anil Kumar Bisht roll/ sr. no.=163

1. WELCOME YOU ALL
Discrete Mathematical Structure
(CS-201N), B.Tech. 2nd Year, III-Sem.
(Session 2020-21)
By:
Er. Anil Kumar Bisht

2. Unit-I
SET THEORY

3. What is a SET?
• A Set is defined as a “well-defined collection” of distinct objects.
• These objects are satisfying a particular property.
• Set theory forms the basis of several other fields of study like relations,
functions and graph theory.
• Objects which belongs to a set are also termed as members or elements of
the set.
• A set is typically expressed by curly braces enclosing its elements.

4. Set Examples
• If A is a set having elements a,e,i,o,u then it is expressed as:
A= {a,e,i,o,u} Finite Set
Suppose, B={ 1,2,3,4,5,6,………..}Infinite Set
• For a set A:
• x  A: x is an element of A
• x  A: x is not an element of A
As seen in above examples for the set A (always uppercase letter) we can
write a ɛ A while ‘b’ does not belongs to this set so it is expressed as b ∉ A.
•

5. Set Notations
• Two forms of notations are there:
• Roster Form: is a list of elements, separated by commas, enclosed in curly braces.
e.g. Y={ 1,2,3,4,5,6,7,8,9,10………..}.  Tabular form.
• Set Builder Form : states the properties that the members of a set must satisfy.
e.g. Y={x: x is a natural number} which means Y is the set that contains all x
such that x is a natural number i.e. property of set is defined here.
• CARDINALITY of a SET: total number of elements in a set.
• So, cardinality of a vowel set is 5 while that of set Y (above case) is infinite.

6. Standard Symbols symbolizing sets of
numbers
• N : The set of all natural numbers (i.e. all positive integers)=infinite +ve
• Z : The set of all integers =infinite in both –ve and +ve directions
including zero
• Q : The set of all rational numbers.
• R : The set of all real numbers
• C : The set of all complex numbers

7. Questions and Answers
• Question: Write down the following sets in tabular form:
• A={x: x is the Female Prime Minister of India}
• B ={x: x is name of days in a week}
• C={x: x5 =32}
• D={x: x2 =4, x is odd}

8. Questions and Answers
• Answer: the given sets in tabular form:
• A={x: x is the Female Prime Minister of India} A={Indira Gandhi}
• B={x: x is name of days in a week} B={Mon, Tue, Wed, Thrs,
Fri, Sat, Sun}
• C={x: x5 =32}  C={2}
• D={x: x2 =4, x is odd}  D={ } or 

9. Questions and Answers
• Question: Write down the following sets in builder form:
• A={2, 4, 6, 8, 10,….}
• B= {2, 4, 6, 8, 10}
• C= {a, b, c, d,……}
• D ={Kapil Dev, Azharuddin, Saurabh Ganguly, Sachin Tendulkar, M S
Dhoni, }

10. Questions and Answers
• Answer: the given sets in builder form:
• A={2, 4, 6, 8, 10,….} A={x: x is an even +ve integer}
• B={2, 4, 6, 8, 10} B={x: x is an even +ve int. & less than equal to 10}
• C={a, b, c, d,……}  C={x: x is a letter in the English Alphabet}
• D={Kapil Dev, Azharuddin, Saurabh Ganguly, Sachin Tendulkar, M S
Dhoni, }  D={x: x have been Captain of Indian Cricket team}

11. Principle of Extension
• Two sets, A and B, are equal if and only if they contain the identical
elements. Then we can write We write A=B.
• e.g.:
A={2,3,4,5}, B={3,5,4,2), C={10∕5,15/5, 20/5, 25/5}, D={2,2,3,4,5,5}
Thus, as per this principle, we can write: A=B=C=D
NOTE: A set remains same or unchanged even if its elements are repeated or rearranged
because a set contains unique elements which are unordered.

12. Thanks to all
Any Queries please….