**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}

(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**

Answer

In Union we write all elements of both sets without repeating.

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

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

**(iii)**Natural number and multiple of 3 are 3, 6, 9 …

Natural number less than 6 are {1, 2, 3, 4, 5, 6}

So we can write A ∪ B as {1, 2, 4, 5, 3, 6, 9, 12 …}

Hence, A ∪ B = {x: x = 1, 2, 4, 5 or a multiple of 3}

**(iv)**Natural numbers grater than 1 and lower than and equal to 6 are 2, 3, 4, 5 and 6.

Natural number greater than 6 and less than 10 are 7, 8 and 9.

So that A∪ B = {2, 3, 4, 5, 6, 7, 8, 9}

Hence, A∪ B = {x: x ∈ N and 1 < x < 10}

**(v)**A = {1, 2, 3}, B = Φ B is a empty set and can be written as B= { } so that A∪ B = {1, 2, 3}

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