# CLASS-11OPERATION 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}

(ivB – 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}

(vC – 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}

(xD – 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}

(xiC – 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.

Symmetric Difference Of Sets,