NCERT Class XI Mathematics - Sets - Solutions
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Question : 38
Total: 73
Which of the following pairs of sets are disjoint?
(i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6}
(ii) {a, e, i, o, u} and {c, d, e, f }
(iii) {x : x is an even integer} and {x : x is an odd integer}
(i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6}
(ii) {a, e, i, o, u} and {c, d, e, f }
(iii) {x : x is an even integer} and {x : x is an odd integer}
Solution:
(i) Let A = {1, 2, 3, 4} and B = {x: x is a natural number and 4 ≤ x ≤ 6} = {4, 5, 6}
∴ A ∩ B = {1, 2, 3, 4} ∩ {4, 5, 6} = {4}
Hence A and B are not disjoint sets.
(ii) Let A = {a, e, i, o, u} and B = {c, d, e, f } ∴ A ∩ B = {e}
Hence A and B are not disjoint sets.
(iii) Let A = {x : x is an even integer} and
B = {x: x is an odd integer} ∴ A ∩ B = ϕ. Hence A and B are disjoint sets.
∴ A ∩ B = {1, 2, 3, 4} ∩ {4, 5, 6} = {4}
Hence A and B are not disjoint sets.
(ii) Let A = {a, e, i, o, u} and B = {c, d, e, f } ∴ A ∩ B = {e}
Hence A and B are not disjoint sets.
(iii) Let A = {x : x is an even integer} and
B = {x: x is an odd integer} ∴ A ∩ B = ϕ. Hence A and B are disjoint sets.
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