# Find the union of each of the following pairs of sets :

(i) X = {1, 3, 5} Y = {1, 2, 3}

(ii) A = [ a, e, i, o, u} B = {a, b, c}

(iii) A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}

(iv) A = {x : x is a natural number and 1 < x ≤ 6 } B = {x : x is a natural number and 6 < x < 10 }

(v) A = {1, 2, 3}, B = φ

**Solution:**

The "union" of two sets is one of the operations on sets and it results in a set that contains the elements of both sets by removing duplicates if any.

Thus,

**(i)** When X = {1, 3, 5} and Y = {1, 2, 3},

**X υ Y = {1, 2, 3, 5}**

**(ii)** When A = {a, e, i, o, u} and B = {a, b, c},

**A υ B = {a , b, c, e, i, o, u}**

**(iii)** A = { x : x is a natural number and multiple of 3} = {3, 6, 9....}

B = { x : x is a natural number less than 6} = {1, 2, 3, 4, 5}

**Then A υ B = {1, 2, 4, 5, 3, 6, 9, 12....}**

**Therefore, A υ B = {x : x = 1, 2, 4, 5 or a multiple of 3}**

**(iv)** A = { x : x is a natural number and 1 < x ≤ 6 } = {2, 3, 4, 5, 6}

B = { x : x is a natural number and 6 < x < 10 } = {7, 8, 9}

**Then A υ B = {2, 3, 4, 5, 6, 7, 8, 9}**

Therefore,

**A υ B = {x : x ∈ N and 1 < x < 10}**

**(v)** When A = {1, 2, 3} and B = Φ,

**A υ B = {1, 2, 3}**

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.4 Question 1

## Find the union of each of the following pairs of sets : (i) X = {1, 3, 5} Y = {1, 2, 3} (ii) A = [ a, e, i, o, u} B = {a, b, c} (iii) A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6} (iv) A = {x : x is a natural number and 1 < x ≤6 } B = {x : x is a natural number and 6 < x < 10 } (v) A = {1, 2, 3}, B = φ

**Summary:**

We are asked to find the union of each of the following pairs of sets. We found that

(i) When X = {1, 3, 5} Y = {1, 2, 3}, X υ Y = {1, 2, 3, 5}

(ii) When A = [ a, e, i, o, u} B = {a, b, c}, A υ B = {a , b, c, e, i, o, u}

(iii) When A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}, A υ B = {x : x = 1, 2, 4, 5 or a multiple of 3}

(iv) When A = {x : x is a natural number and 1 < x ≤ 6 } B = {x : x is a natural number and 6 < x < 10 }, A υ B = {2, 3, 4, 5, 6, 7, 8, 9}

(v) When A = {1, 2, 3}, B = φ, A υ B = {1, 2, 3}