Operations on Sets:-

Just as operations of addition, subtraction etc., are performed on numbers, the
operations of unions, intersection etc., are performed on sets. We are already familiar with
them. A review of the main rules is given below: –
Union of two sets: The Union of two sets A and B, denoted by A\cup B, is the set of all elements,
which belong to A or B.

Symbolically;

A\cup B={{\;x/x\in A\;\vee\;x\in B}}
Thus if A= \left { 1,2,3 \right } , B=\left ] 2,3,4,5 \right }[/katex]

A\cup B =\left { 1,2,3,4,5 \right }

Intersection of two sets:

The intersection of two sets A and B, denoted by A\cap B, is the set
of all elements, which belong to both A and B.

Symbolically;

Disjoint Sets:

If the intersection of two sets is the empty set then the sets are said to be
disjoint sets.

For example;

If S_{1}= The set of odd natural numbers and S_{2}= The set of even natural numbers, then S_{1} and S_{2}
are disjoint sets.

The set of arts students and the set of science students of a
college are disjoint sets.

Overlapping sets:

If the intersection of two sets is non-empty but neither is a subset of the
other, the sets are called overlapping sets, e.g., if
L = {2,3,4,5,6} and M= {5,6,7,8,9,10}, then L and M are two overlapping sets

Complement of a set:

The complement of a set A, denoted by A^{'} or A^{c}
relative to the universal
set U is the set of all elements of U, which do not belong to A.
Symbolically:

A^{'} =\left { x/x\in U\wedge x\notin A \right }[/katex]
For example, if U=N, then E^{'} = O and O^{'}=E

Example 1:

If U = set of alphabets of English language,
C = set of consonants,
W = set of vowels, then C^{'}= W and W^{'}= C

Difference of two Sets:

The Difference set of two sets A and B denoted by A-B consists of
all the elements which belong to A but do not belong to B.
The Difference set of two sets B and A denoted by B-A consists of all the elements, which
belong to B but do not belong to A.
Symbolically, A-B = { } xx A x B ∈ ∧∉ and B-A = { } xx B x A ∈ ∧∉
Example 2: If A = {1,2,3,4,5}, B = {4,5,6,7,8,9,10}, then
A-B = {1,2,3} and B-A = {6,7,8,9,10}

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Azhar Ali

Azhar Ali

I graduated in Mathematics from the University of Sargodha, having master degree in Mathematics.

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