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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 

1 Answer

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(i) X = {1, 3, 5} Y = {1, 2, 3}
 X ∪ Y= {1, 2, 3, 5}
(ii) A = {a, e, i, o, u} B = {a, b, c}
 A ∪ 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, 6}
A ∪ B = {1, 2, 4, 5, 3, 6, 9, 12 …}
∴ A ∪ 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}
A ∪ B = {2, 3, 4, 5, 6, 7, 8, 9}
∴ A∪ B = {x: x ∈ N and 1 < x < 10}
(v) A = {1, 2, 3}, B = Φ
A ∪ B = {1, 2, 3}

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