NCERT Class XI Mathematics - Sets - Solutions
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Question : 10
Total: 73
In the following, state whether A = B or not:
(i) A = {a, b, c, d} ; B = {d, c, b, a}
(ii) A = {4, 8, 12, 16} ; B = {8, 4, 16, 18}
(iii) A = {2, 4, 6, 8, 10} B = {x : x is positive even integer and x ≤ 10}
(iv) A = {x : x is a multiple of 10} B = {10, 15, 20, 25, 30, . . . }
(i) A = {a, b, c, d} ; B = {d, c, b, a}
(ii) A = {4, 8, 12, 16} ; B = {8, 4, 16, 18}
(iii) A = {2, 4, 6, 8, 10} B = {x : x is positive even integer and x ≤ 10}
(iv) A = {x : x is a multiple of 10} B = {10, 15, 20, 25, 30, . . . }
Solution:
(i) A = {a, b, c, d} and B = {d, c, b, a} are equal sets because order of elements does not changes a set.
∴ A = B = {a, b, c, d}.
(ii) A = {4, 8, 12, 16} and B = {8, 4, 16, 18} are not equal sets because 12 ∈ A but 12 ∉ B and 18 ∈ B but 18 ∉ A.
(iii) A = {2, 4, 6, 8, 10} and B = {x: x is a positive even integer and x ≤ 10} which can be written in roster form as B = {2, 4, 6, 8, 10} are equal sets.
∴ A = B = {2, 4, 6, 8, 10}.
(iv) A = {x: x is a multiple of 10} can be written in roster form as A = {10, 20, 30, 40, ......} and B = {10, 15, 20, 25, 30, .....} are not equal sets because 15 ∈ B but 15 ∉ A.
∴ A = B = {a, b, c, d}.
(ii) A = {4, 8, 12, 16} and B = {8, 4, 16, 18} are not equal sets because 12 ∈ A but 12 ∉ B and 18 ∈ B but 18 ∉ A.
(iii) A = {2, 4, 6, 8, 10} and B = {x: x is a positive even integer and x ≤ 10} which can be written in roster form as B = {2, 4, 6, 8, 10} are equal sets.
∴ A = B = {2, 4, 6, 8, 10}.
(iv) A = {x: x is a multiple of 10} can be written in roster form as A = {10, 20, 30, 40, ......} and B = {10, 15, 20, 25, 30, .....} are not equal sets because 15 ∈ B but 15 ∉ A.
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