Question

If U = {x / x ∈ N, 1 ≤ x ≤ 12} A = {1, 4, 7, 10} B = {2, 4, 6, 7, 11) C = {3, 5, 8, 9, 12} Write down the sets
i) A∪B
ii) B∩C
iii) A - B
iv) B∩C'
v) A∪B∪C
vi) A∩(B∪C)

Answer 1

it is given that, U = {x / x ∈ N, 1 ≤ x ≤ 12}

e.g., U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A = {1, 4, 7, 10} , B = {2, 4, 6, 7, 11} and C = {3, 5, 8, 9, 12}

i) $A\cup B$

$\cup$ is symbol of union. $A\cup B$ means set of all elements which contains A or B

so, {1, 4, 7, 10} $\cup$ {2, 4, 6, 7, 11}

= {1, 2, 4, 6, 7, 10, 11}

ii) $B\cap C$

$\cap$ is symbol of intersection. $B\cap C$ means set of all elements which contains common elements of B and C.

so, {2, 4, 6, 7, 11} $\cap$ {3, 5, 8, 9, 12}

= $\Phi$

iii) A - B or A complement B

= {1, 4, 7, 10} - {2, 4, 6, 7, 11}

= {1, 10}


iv) B∩C'

{2, 4, 6, 7, 11} ∩ C'

we know, C' = U - C
= {1, 2,. .. 12} - {3, 5, 8, 9, 12}
= {1, 2, 4, 6, 7, 10, 11}

now, {2, 4, 6, 7, 11} ∩ {1, 2, 4, 6, 7, 10, 11}

= {2, 4, 6 7, 11}


v) A U B U C

= {1, 4, 7, 10} U {2, 4, 6, 7, 11} U {3, 5, 8, 9, 12}

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} = U

vi) A ∩ (B U C)

= {1, 4, 7, 10} ∩ [{2,4, 6, 7, 11} U {3, 5, 8, 9, 12} ]

= {1, 4, 7, 10} ∩ [{2, 3, 4, 5, 6, 7, 8, 9, 11, 12} ]

= {4, 7 }