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Question

Find the union of each of the following pair 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<x6} B={x:x is a natural number and 6<x<10}
(v) A={1,2,3},B=ϕ

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Solution

Given: x={1,3,5},y={1,2,3}
The union of x and y is the set which consists of all the elements of x as well as y, the common elements being taken only once.
xy={1,2,3,5}

Given: A={a,e,i,o,u},B={a,b,c}
The union of A and B is the set which consists of all the elements of A as well as B, the common elements being taken only once.
AB={a,b,c,e,i,o,u}

Given: A={x:x is a natural number and multiple of 3}
A={3,6,9,12,}
B={x:x is a natural number less than 6}
B={1,2,3,4,5}
Hence, AB={1,2,3,4,5,6,9,12,...}
or AB={x:x=1,2,3,4,5 or a multiple of 3}

Given: A={x:x is a natural number and 1<x6}
A={2,3,4,5,6}
B={x:x is a natural number and 6<x<10}
B={7,8,9}
Hence, AB={2,3,4,5,6,7,8,9}
or AB={x:xN and 1<x<10}

Given: A={1,2,3},B=ϕ
The union of A and B is the set which consists of all the elements of A as well as B, the common elements being taken only once.
AB={1,2,3}

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