Question

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

Answer 1

i) A - B = {3,6,9,15,18,21}
ii) A-C ={3,9,15,18,21}
iii) A- D = {3,6,9,12,18,21}
iv) B-A = {4,8,16,20}
v) C- A = {2,4,8,10,14,16}
vi) D- A = {3,6,9,12,18,21}
vii) B- C = {20}
viii) B - D = {4,8,12,16}
ix) C- B = {2,6,10,14}
x) D - B = {4,8,12,16}

Answer 2

Concept-

This question is based on sets . The concept of sets is very simple. It is a suffix as the basis on which all abstract notions in mathematics can be built. A set is determined by its elements . If A is a set , we write x∈ A to say that x is an element of A.

Given-

Elements present in sets A, B, C AND D are as follows:

A = { 3, 6 , 9 , 12 , 15 , 18 , 21 }

B= { 4 , 8 , 12 , 16 , 20 }

C= { 2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 }

D= { 5 , 10 , 15 , 20 }

Find-

We have to find A-B, A-C , C-B , B-D.

Solution-

(i) A-B

A-B = A - (A∩B)

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

A∩B = { 12}

A-B = A- (A∩B)

A-B = { 3, 6 ,9 , 12 , 15 , 18 , 21 } - {12 }

A-B = {3 , 6 , 9 , 15 , 18 , 21 }

Hence, A-B = {3 , 6 , 9 , 15 , 18 , 21 }

(ii) A-C

A-C = A - (A∩C)

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

A∩C = {6 , 12}

A-C = A - (A∩C)

A-C= { 3, 6 , 9 , 12 , 15 , 18 , 21 } -  { 6 , 12}

A-C = {3 , 9 , 15 , 18 , 21}

Hence, A-C = {3 , 9 , 15 , 18 , 21}

(iii) C-B

C-B = C - (C∩B)

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

C∩B = {4 , 8 , 12 , 16}

C-B = C - (C∩B)

C-B =  { 2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 } -  {4 , 8 , 12 , 16}

C-B = {2 , 6 , 10 , 14}

Hence, C-B = {2 , 6 , 10 , 14}

(iv) B-D

B-D = B- (B∩D)

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

B∩D = {20}

B-D = B- (B∩D)

B-D =  { 4 , 8 , 12 , 16 , 20 } - {20}

B-D = { 4, 8 , 12 , 16 }

Hence, B-D = { 4, 8 , 12 , 16 }

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