Question

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 = \(\phi\)

Answer 1

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

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

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

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

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(v) A = {1, 2, 3}, B =\(\phi\)
\(A ∪ B\) = {1, 2, 3}