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<x≤6} 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. ∴x∪y={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. ∴A∪B={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, A∪B={1,2,3,4,5,6,9,12,...} or A∪B={x:x=1,2,3,4,5 or a multiple of 3} Given: A={x:x is a natural number and 1<x≤6} ∴A={2,3,4,5,6} B={x:x is a natural number and 6<x<10} ∴B={7,8,9} Hence, A∪B={2,3,4,5,6,7,8,9} or A∪B={x:x∈N 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. ∴A∪B={1,2,3}

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