Which of the following pairs of sets are ...

NCERT Class XI Mathematics - Sets - Solutions

Question : 38 of 73

Marks: +1, -0

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}

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.

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