LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

OPERATION ON SETS - DIFFERENCE OF SETS

**Difference
Of Sets –**

**(1) Let, A and B be two sets. Then the set of all elements
of A which belong to A but do not belongs to B is called the difference of sets
A and B and is denoted by A – B.**

**(2) The set of all elements which belong to B but do not belong
to A is called the difference of sets B and A and is denoted by B – A. Thus**

** A – B = {x ǀ
x ∈ A, x ∉ B}**

** B – A = {x ǀ x ∈ B, x ∉ A}**

**For Example –**

**(i) Let A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, **

** then
A – B = {1, 2}, B – A = {6, 7}**

**Please note, A – B ≠ B – A **

**(ii) Let A = {1, 3, 5, 7, 9, 11,
13, 15}, B = {3, 5, 7, 9} **

** then A – B = {1, 11, 13, 15}, B – A = ϕ.**

**Please note, A – B ≠ B – A**

**Please note, the difference of
sets A & B is also denoted by A / B.**

**Example.1) If A = {3, 6, 9, 12,
15, 18, 21, 24, 27, 30}, B = {4, 8, 12, 16, 20, 24, 28, 32}, C = {2, 4, 6, 8,
10, 12, 14, 16, 18, 20, 22, 24}, and D = {5, 10, 15, 20, 25, 30, 35} **

**(i) A – B **

**Ans.) A – B = {the element which are in A but not
in B}**

** = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30} – {4,
8, 12, 16, 20, 24, 28, 32}**

** = {3, 6, 9, 15, 18, 21,
27, 30}**

**(ii) A – C**

**Ans.) A – C
= {the elements which are in A but not in C}**

** = {3,
6, 9, 12, 15, 18, 21, 24, 27, 30} – {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22,
24}**

** = {3,
6, 9, 15, 21, 27, 30}**

**(iii) A – D **

**Ans.) A – D
= {the elements which are in A but not in D}**

** = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30} – {5,
10, 15, 20, 25, 30, 35}**

** = {3, 6, 9, 12, 18, 21, 24, 27}**

**(iv) B – A **

**Ans.) B – A = {the elements which are in B but not in A}**

** = {4, 8, 12, 16, 20, 24, 28, 32} – {3, 6, 9,
12, 15, 18, 21, 24, 27, 30}**

** = {4, 8, 16, 20, 28, 32}**

**(v) C – A **

**Ans.) C – A = {the elements which are in C but not
in A}**

** = {2, 4, 6, 8, 10, 12,
14, 16, 18, 20, 22, 24} – {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}**

** = {2, 4, 8, 10, 14, 16, 20, 22}**

**(vi) D – A**

**Ans.) D – A = {the elements which are in D but not
in A}**

** = {5, 10, 15, 20, 25,
30, 35} – {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}**

** = {5, 10, 20, 25, 35}**

**(vii) B – C**

**Ans.) B – C = {the elements which are in B but
not in C}**

** = {4, 8, 12, 16, 20, 24, 28, 32} – {2, 4, 6, 8,
10, 12, 14, 16, 18, 20, 22, 24}**

** = {20, 28, 32}**

**(viii) B – D **

** B – D =
{the elements which are in B but not in D}**

** = {4, 8, 12, 16, 20, 24, 28, 32} – {5, 10, 15,
20, 25, 30, 35}**

** = {4, 8, 12, 16, 24, 28, 32}**

**(ix) C – B **

**Ans.) C – B = {the elements which are in C but not
in B}**

** = {2, 4, 6, 8, 10, 12,
14, 16, 18, 20, 22, 24} – {4, 8, 12, 16, 20, 24, 28, 32}**

** = {2, 6, 10, 14, 18, 22}**

**(x) D – B **

**Ans.) D – B = {the elements which are in D but not
in B}**

** = {5, 10, 15, 20, 25,
30, 35} – {4, 8, 12, 16, 20, 24, 28, 32}**

** = {5, 10, 15, 25, 30, 35}**

**(xi) C – D **

**Ans.) C – D = {the elements which are in C but not
in D}**

** = {2, 4, 6, 8, 10, 12, 14,
16, 18, 20, 22, 24} – {5, 10, 15, 20, 25, 30, 35}**

** = {2, 4, 6, 8, 12, 14, 16, 18, 22, 24}**

**(xii) D – C **

**Ans.) D – C = {the elements which are in D but
not in C}**

** = {5, 10, 15, 20, 25, 30, 35} – {2, 4, 6, 8,
10, 12, 14, 16, 18, 20, 22, 24}**

** = {5, 15, 25, 30, 35}**

**Properties
Of Difference Of Sets.**

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