Question

9. IfA-13, 6, 9, 12, 15, 18, 21), B 14, 8, 12, 16, 20 ),C= { 2, 4, 6, 8, 10, 12, 14, 16 }, D= {5, 10, 15, 20 }; find(G) A - B(v) C-A(vi) D(ix)A-C-AD-B(ii) A D iv) B-A(vii) B- C v) B D(ii)Vi1ViliC-B(x)

Answer 1

Given, A={ 3,6,9,12,15,18,21 } , B={ 4,8,12,16,20 } , C={ 2,4,6,8,10,12,14,16 } and D={ 5,10,15,20 } .

(i)

A−B means that the set contains elements of set A but not of set B .

So, set A−B can be expressed as

A−B=A−( A∩B ) ={ 3,6,9,12,15,18,21 }−( { 3,6,9,12,15,18,21 }∩{ 4,8,12,16,20 } ) ={ 3,6,9,12,15,18,21 }−{ 12 } ={ 3,6,9,15,18,21 }

Hence, A−B={ 3,6,9,15,18,21 } .

(ii)

A−C means that the set contains elements of set A but not of set C .

So, set A−C can be expressed as

A−C=A−( A∩C ) ={ 3,6,9,12,15,18,21 }−( { 3,6,9,12,15,18,21 }∩{ 2,4,6,8,10,12,14,16 } ) ={ 3,6,9,12,15,18,21 }−{ 6,12 } ={ 3,9,15,18,21 }

Hence, A−C={ 3,9,15,18,21 } .

(iii)

A−D means that the set contains elements of set A but not of set D .

So, set A−D can be expressed as

A−D=A−( A∩D ) ={ 3,6,9,12,15,18,21 }−( { 3,6,9,12,15,18,21 }∩{ 5,10,15,20 } ) ={ 3,6,9,12,15,18,21 }−{ 15 } ={ 3,6,9,12,18,21 }

Hence, A−D={ 3,6,9,12,18,21 } .

(iv)

B−A means that the set contains elements of set B but not of set A .

So, set B−A can be expressed as

B−A=B−( B∩A ) ={ 4,8,12,16,20 }−( { 4,8,12,16,20 }∩{ 3,6,9,12,15,18,21 } ) ={ 4,8,12,16,20 }−{ 12 } ={ 4,8,16,20 }

Hence, B−A={ 4,8,16,20 } .

(v)

C−A means that the set contains elements of set C but not of set A .

So, set C−A can be expressed as

C−A=C−( C∩A ) ={ 2,4,6,8,10,12,14,16 }−( { 2,4,6,8,10,12,14,16 }∩{ 3,6,9,12,15,18,21 } ) ={ 2,4,6,8,10,12,14,16 }−{ 6,12 } ={ 2,4,8,10,14,16 }

Hence, C−A={ 2,4,8,10,14,16 } .

(vi)

D−A means that the set contains elements of set D but not of set A .

So, set D−A can be expressed as

D−A=D−( D∩A ) ={ 5,10,15,20 }−( { 5,10,15,20 }∩{ 3,6,9,12,15,18,21 } ) ={ 5,10,15,20 }−{ 15 } ={ 5,10,20 }

Hence, D−A={ 5,10,20 } .

(vii)

B−C means that the set contains elements of set B but not of set C .

So, set B−C can be expressed as

B−C=B−( B∩C ) ={ 4,8,12,16,20 }−( { 4,8,12,16,20 }∩{ 2,4,6,8,10,12,14,16 } ) ={ 4,8,12,16,20 }−{ 4,8,12,16 } ={ 20 }

Hence, B−C={ 20 } .

(viii)

B−D means that the set contains elements of set B but not of set D .

So, set B−D can be expressed as

B−D=B−( B∩D ) ={ 4,8,12,16,20 }−( { 4,8,12,16,20 }∩{ 5,10,15,20 } ) ={ 4,8,12,16,20 }−{ 20 } ={ 4,8,12,16 }

Hence, B−D={ 4,8,12,16 } .

(ix)

C−B means that the set contains elements of set C but not of set B .

So, set C−B can be expressed as

C−B=C−( B∩C ) ={ 2,4,6,8,10,12,14,16 }−( { 4,8,12,16,20 }∩{ 2,4,6,8,10,12,14,16 } ) ={ 2,4,6,8,10,12,14,16 }−{ 4,8,12,16 } ={ 2,6,10,14 }

Hence, C−B={ 2,6,10,14 } .

(x)

D−B means that the set contains elements of set D but not of set B .

So, set D−B can be expressed as

D−B=D−( B∩D ) ={ 5,10,15,20 }−( { 4,8,12,16,20 }∩{ 5,10,15,20 } ) ={ 5,10,15,20 }−{ 20 } ={ 5,10,15 }

Hence, D−B={ 5,10,15 } .

(xi)

C−D means that the set contains elements of set C but not of set D .

So, set C−D can be expressed as

C−D=C−( C∩D ) ={ 2,4,6,8,10,12,14,16 }−( { 2,4,6,8,10,12,14,16 }∩{ 5,10,15,20 } ) ={ 2,4,6,8,10,12,14,16 }−{ 10 } ={ 2,4,6,8,12,14,16 }

Hence, C−D={ 2,4,6,8,12,14,16 } .

(xii)

D−C means that the set contains elements of set D but not of set C .

So, set D−C can be expressed as

D−C=D−( C∩D ) ={ 2,4,6,8,10,12,14,16 }−( { 2,4,6,8,10,12,14,16 }∩{ 5,10,15,20 } ) ={ 5,10,15,20 }−{ 10 } ={ 5,15,20 }

Hence, D−C={ 5,15,20 } .