Q. 9
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:
(i) A – B
(ii) A – C
(iii) A – D
(iv) B – A
(v) C – A
(vi) D – A
(vii) B – C
(viii) B – D
(ix) C – B
(x) D – B
(xi) C – D
(xii) D – C
Answers
Step-by-step explanation:
A - B shows the relative complement of the set, which represents members of set A which are not part of set B
refer the image
(i) It is given in the question that,
A = {3, 6, 9, 12, 15, 18, 21}
And, B = {4, 8, 12, 16, 20}
∴ A – B = {3, 6, 9, 12, 15, 18, 21} - {4, 8, 12, 16, 20}
12 is present in both the sets, so A - B will not contain 12 and will contain rest of the elements of A
= {3, 6, 9, 15, 18, 21}
(ii) It is given in the question that,
A = {3, 6, 9, 12, 15, 18, 21}
And, C = {2, 4, 6, 8, 10, 12, 14, 16}
∴ A – C = {3, 6, 9, 12, 15, 18, 21} - {2, 4, 6, 8, 10, 12, 14, 16}
= {3, 9, 15, 18, 21}
(iii) It is given in the question that,
A = {3, 6, 9, 12, 15, 18, 21}
And, D = {5, 10, 15, 20}
∴ A – D = {3, 6, 9, 12, 15, 18, 21} - {5, 10, 15, 20}
= {3, 6, 9, 12, 18, 21}
(iv) It is given in the question that,
B = {4, 8, 12, 16, 20}
And, A = {3, 6, 9, 12, 15, 18, 21}
∴ B – A = {4, 8, 12, 16, 20} - {3, 6, 9, 12, 15, 18, 21}
= {4, 8, 16, 20}
(v) It is given in the question that,
C = {2, 4, 6, 8, 10, 12, 14, 16}
And, A = {3, 6, 9, 12, 15, 18, 21}
∴ C – A = {2, 4, 6, 8, 10, 12, 14, 16} - {3, 6, 9, 12, 15, 18, 21}
= {2, 4, 8, 10, 14, 16}
(vi) It is given in the question that,
D = {5, 10, 15, 20}
And, A = {3, 6, 9, 12, 15, 18, 21}
∴ D – A = {5, 10, 15, 20} - {3, 6, 9, 12, 15, 18, 21}
= {5, 10,20}
(vii) It is given in the question that,
B = {4, 8, 12, 16, 20}
And, C = {2, 4, 6, 8, 10, 12, 14, 16}
∴ B – C = {4, 8, 12, 16, 20} - {2, 4, 6, 8, 10, 12, 14, 16}
= {20}
(viii) It is given in the question that,
B = {4, 8, 12, 16, 20}
And, D = {5, 10, 15, 20}
∴ B – D = {4, 8, 12, 16, 20} - {5, 10, 15, 20}
= {4, 8, 12, 16}
(ix) It is given in the question that,
C = {2, 4, 6, 8, 10, 12, 14, 16}
And, B = {4, 8, 12, 16, 20}
∴ C – B = {2, 4, 6, 8, 10, 12, 14, 16} - {4, 8, 12, 16, 20}
= {2, 6, 10, 14}
(x) It is given in the question that,
D = {5, 10, 15, 20}
And, B = {4, 8, 12, 16, 20}
∴ D – B = {5, 10, 15, 20} - {4, 8, 12, 16, 20}
= {5, 10, 15}
(xi) It is given in the question that,
C = {2, 4, 6, 8, 10, 12, 14, 16}
And, D = {5, 10, 15, 20}
∴ C – D = {2, 4, 6, 8, 10, 12, 14, 16} - {5, 10, 15, 20}
= {2, 4, 6, 8, 12, 14, 16}
(xii) It is given in the question that,
D = {5, 10, 15, 20}
And, C = {2, 4, 6, 8, 10, 12, 14, 16}
∴ D – C = {5, 10, 15, 20} - {2, 4, 6, 8, 10, 12, 14, 16}
= {5, 15, 20}
JAI SHREE KRISHNA
