1. A set is a collection of well-defined objects called elements. Sets can be represented in roster form by listing elements within curly brackets or in set-builder form describing a common property of elements. 2. Sets can be finite, containing a countable number of elements, or infinite with an uncountable number. The number of elements in a set is its cardinal number. 3. Important set operations include union, intersection, difference, and complement. Venn diagrams provide a visual representation of relationships between sets.

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2.Sets

2. 2.Sets
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2.Sets
1) Set : The collection of well defined objects is called a set. The objects in a set are
called elements.
Eg. A={p,q,r,s} and B={All students of a class}
2) Roaster form: If all the elements of a set are listed and enclosed in the brackets { },
then we say the set is in the roaster form.
3) Set Builder form : In this method elements are described by their common property
i.e. A set is denoted as {x/x satisfies p(x) where p(x) is the common property}
4) Finite set: If the number of elements in a set are finite, then the set is called as finite
set. Eg: set of days in a week
5) Infinite set: A set which contains un counting of elements is called infinite set.
N={1,2,3,4……..}
6) Cardinal number: The number of different elements in a set is known as its cardinal
number. It is denoted by If .
7) Equal sets: Two sets A and B are said to be equal if they contain same elements.
Eg: A={1,2,3} and B={2,4,6}
8) Equivalent sets: Two sets A and B are ssaid to be equivalent if the number of
elements in two sets are the same Eg: A={1,2,3} and B={2,4,6}
9) Null set: a set containing no elements is called an empty set or null set or void test. It
is denoted by
10) Singleton set : a set containing only one element is called singleton set
Eg. A set of even prime numbers ={2}
11) Subset: A set A is called subset of a set B if every element of A is in B. It is denoted
by . In this case B is called super set of A.
12) Proper subset: a set A is called proper subset of B if and . It is
denoted by
13) If there are n elements in a set the number of subsets of that set is .
14) If there are n elements in a set the number of proper subsets of that set is .
15) Power set: The set of all subsets of set A is called power set of A. It is denoted by
. If A contains n different elements the contains different elements.

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16) Union of sets: The set containing the elements of A and B or both is called as union
of sets. It is denoted by . { / .
17) Intersection of sets: The set containing the elements of A and B which are common
in both sets A and B is called as intersection of sets. It is denoted by .
{ / .
18) Universal set: The set under consideration are all subsets of a fixed set, then the
fixed set is called universal set and it is denoted by .
19) The difference of two sets A,B is denoted as A-B or B-A
20) Venn diagrams are a convenient way of showing operations between sets.
21) Disjoint sets: If the intersection of two sets is a null set,, then they are called as
disjoint sets.
Some Important Laws on Sets
 Idempotent Law :
 Associative Law:
 Commutative Law: and
 Distributive Law:
Some Important Results
i.
ii. If then If then
iii. If then
iv. If then
v.
vi.
vii.
viii. If then
ix.

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Multiple Choice Questions
1) If and and represents P then
(a) 1 (b)2 (c)3 (d)0
2) If then
(a) 22 (b)39 (c)24 (d)51
3) If A and B are disjoint sets, then
(a) (b) (c) (d)None
4) If and
Then
(a) A (b)B (c)C (d)
5) If and then
(a) (b) (c) (d)
6) Which of the following is an empty set
(a) The set of all lines passing through a point
(b) is an odd number divisible by
(c) ) is a common point to any two parallel lines}
(d)
7) A is the set of all factors of 24. B is the set of all factors of 48. Then
(a) (b) (c) (d)
8) . It is ___________ Law
(a) Identity (b)Complement (c)Idempotent (d) commutative
9) {multiples of 2} multiples of then
(a) Set of multiples of 5 (b)set of multiples of 9
(c) set of multiples of 4 (d) Set of multiples of 6
10) If then
(a) (b)
(c) (d)
11) then
(a) (b)
(c) (d) None

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12) . This property is called
(a) Reflexive property (b)symmetric property
(c) anti symmetric property (d) transitive property
13) If then the number of proper subsets of A
(a) 31 (b)26 (c)35 (d
14) If there are four elements in a set, then number of proper subsets that can be
written
(a) (b) (c) (d)
15) If ; then which of the following is true
(a) (b) (c) (d)
16) N of l t th wo d “SUCCESS”
(a) (b) (c) (d)
17)
(a) (b) (c) (d)
18) then
(a) (b) (c) (d)
19) is a real number then
(a) (b) (c) (d)
20) If then
(a) (b) (c)c ’t d f d (d) None
21)
(a) (b)
(c) (d)
22) If A,B and C are non collinear points, then is
(a) (b) (c) (d)
23) set builder form of A is
(a) (b)
(c) (d) None
24) P is a non empty set and is an empty set then
(a) (b) (c)P (d)

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25) If then
(a) (b) (c) (d)
26)
(a) (b) (c) (d)
27) Which of the following is a finite set
(a) Set of odd numbers (b)Set of even numbers
(c) Set of continents in the world (d) set of multiples of 3
28) . This is
(a) commutative property (b)idempotent property
(c)Distributive property (d) Associative property
29)
(a) (b)
(c) (d)
30) Out of 100 students, 50 fail in English and 30 fail in mathematics. If 2 students fail I
both English and Mathematics, the number of students passing in both these
subjects
(a) (b) (c) (d)
Answers
1 2 3 4 5 6 7 8 9 10
a d a d a b a c d a
11 12 13 14 15 16 17 18 19 20
c b a d c b b c d a
21 22 23 24 25 26 27 28 29 30
b a b c b b c d a a