Difference of Sets using Venn Diagram (advance math)

Created with Sketch.

Difference of Sets using Venn Diagram

 

How to find the
difference of sets using Venn diagram?

The difference of two subsets A and B is a
subset of U, denoted by A – B and is defined by

A – B = {x : x ∈
A and x ∉ B}.

Let A and B be two sets. The difference of
A and B, written as A – B, is the set of all those elements of A which do not
belongs to B.

Thus A – B = {x : x ∈
A and x ∉ B} or A – B = {x ∈
A : x ∉ B}.

Clearly, x ∈
A – B

⇒ x ∈
A and x ∉ B

In the adjoining figure the shaded part
represents A – B.

Difference of Sets using Venn Diagram

Similarly, the difference B – A is the set
of all those elements of B that do not belongs to A.

Thus, B – A = {x :
x ∈ A and x ∉ B} or A – B = {x ∈
B : x ∉ A}.


In the adjoining figure the shaded part represents B – A.

Difference of Sets Venn Diagram

In particular, A – B = ∅ if A ⊂ B and A –
B = A if A ∩ B = ∅.

The subset of A – B is also called the
complement of B relative to A.

The difference A – B can be expressed in
terms of the complement as A – b = A ∩
B’.

Properties of difference of sets:

1. A – (B ∩ C) = (A – B) ∪ (A – C)

2. A – (B ∪ C) = (A – B) ∩ (A – C)

 

 

Solved example to find the
difference of sets using Venn diagram
:

1.
If A = {2, 3, 4, 5, 6, 7} and B = {3, 5, 7, 9, 11, 13}, then find (i) A – B and
(ii) B – A.

Solution:

According to the given statement; A = {2,
3, 4, 5, 6, 7} and B = {3, 5, 7, 9, 11, 13}

(i) A – B

Difference of Sets

= {2, 4, 6}

 

(ii) B – A

Difference of Two Sets

= {9, 11, 13}

 

2.
Given three sets A, B and C such that: A = {x : x is a natural number between
10 and 16}, B = {set of even numbers between 8 and 20} and C = {7, 9, 11, 14,
18, 20}.

Find the difference
of sets using Venn diagram:

(i) A – B

(ii) B – C

(iii) C – A

(iv) B – A

Solution:

According to the given statement

A = {11, 12, 13, 14, 15}

B = {10, 12, 14, 16, 18}

C = {7, 9, 11, 14, 18, 20}

 

(i) A – B

Shaded Part Represents B – A

= {Those elements of set A which are not
in set B}

= {11, 13, 15}

 

(ii) B – C

Difference of Set A and Set B

= {Those elements of set B which are not
in set C}

= {10, 12, 16}

 

(iii) C – A

Find the Difference of Sets

= {Those elements of set C which are not
in set A}

= {7, 9, 18, 20}

 

(iv) B – A

Difference of Sets Example

= {Those elements of set B which are not
in set A}

= {10, 16, 18}

 

Leave a Reply

Your email address will not be published. Required fields are marked *

This is a free online math calculator together with a variety of other free math calculatorsMaths calculators
+