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NCERT Class 11 Notes Maths
Chapter 1 sets
By shahigem,
Set
A set is a well-defined collection of objects
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Roster or Tabular form In the roster form, we
list all the members of the set within braces { }
and separate by commas
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Set-builder form In the set-builder form, we list
the property or properties satisfied by all the
elements of the sets
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Singleton Set: A set consists of a single element,
is called a singleton set
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Equal Sets: Two sets A and B are said to be
equal, if every element of A is also an element of
B or vice-versa, i
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two equal sets will have
exactly the same element

Equivalent Sets: Two finite sets A and B are said
to be equal if the number of elements are equal,
i
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n(A) = n(B)

Subset
A set A is said to be a subset of set B if every
element of set A belongs to set B
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Every set is o subset of itself
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The empty set is a subset of every set
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The total number of subsets of a finite set
containing n elements is 2^n
Intervals as Subsets of R
Let a and b be two given real numbers such that
a < b, then

     1
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     2
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     3
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Power Set
The collection of all subsets of a set A is called
the power set of A
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If the
number of elements in A i
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n(A) = n, then the
number of elements in P(A) = 2^n
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Venn-Diagrams
Venn diagrams are the diagrams, which represent
the relationship between sets
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Operations of Sets
Union of sets: The union of two sets A and B,
denoted by A ∪ B is the set of all those elements
which are either in A or in B or in both A and B
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Intersection of sets: The intersection of two sets
A and B, denoted by A ∩ B, is the set of all

elements which are common to both A and B
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Intersecting or Overlapping sets: Two sets A and
B are said to be intersecting or overlapping if A ∩
B≠Φ
Difference of sets: For any sets A and B, their
difference (A – B) is defined as a set of elements,
which belong to A but not to B
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Then, the complement of
A is the set of all elements of U which are not the

element of A
Thus, A’ = U – A = {x : x ∈ U and x ∉ A}

Some Properties of Complement of Sets
A ∪ A’ = ∪
A ∩ A’ = Φ
∪’ = Φ
Φ’ = ∪
(A’)’ = A
Symmetric difference of two sets: For any set A
and B, their symmetric difference (A – B) ∪ (B –
A)
(A – B) ∪ (B – A) defined as set of elements
which do not belong to both A and B
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Thus, A Δ B = (A – B) ∪ (B – A) = {x : x ∉ A ∩ B}
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