# 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:**

A pair of sets is said to be disjoint when there are no common elements in them.

i.e., two sets A and B are said to be disjoint if A ∩ B = Φ.

(i) The first set is {1, 2, 3, 4}

The second set is {x : x is a natural number and 4 ≤ x ≤ 6}

= {4, 5, 6}

Now,

{1, 2, 3, 4} ∩ {4, 5, 6} = {4} ≠ Φ

Therefore, this pair of sets is NOT disjoint.

(ii) {a, e, i, o, u} ∩ {c, d, e, f} = {e} ≠ Φ

Therefore, this pair of sets are NOT disjoint.

(iii) {x : x is an even integer} ∩ {x : x is an odd integer} = Φ because there is no integer which can be both even and odd.

Therefore, this pair of sets is disjoint

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.4 Question 8

## 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}

**Summary:**

We are asked to find which of the given pairs of sets are disjoint. We found that

(i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6 } are **NOT disjoint**

(ii) {a, e, i, o, u} and {c, d, e, f} are **NOT disjoint**

(iii) {x : x is an even integer} and {x : x is an odd integer} are **disjoint**

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