Question

Let U= {1, 2, 3, 4,5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B= {2, 4, 6, 8} and C={3, 4, 5, 6} Find $(A^{'})^ {'}$

Answer 1

we know, complement of set , A' = U - A
so, (A' )' = (U - A)' = U - (U - A) = U - U + A = A
hence, ( A ') ' = A

[complement of set C means set of that elements that do not belong to C. ]

here given,
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 3, 4}

so, (A')' = A = {1, 2, 3, 4}

Answer 2

Solution :

Given U = { 1,2,3,4,5,6,7,8,9 }

A = { 1,2,3,4 } ,

B = { 2,4,6,8 },

C = { 3,4,5,6 }

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A' ={x:x€U and x doesn't belongs to A}

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i ) A' = U - A

= { 1,2,3,4,5,6,7,8,9 } - { 1,2,3,4 }

= { 5,6,7,8,9 }

ii ) ( A' )' = U - A'

= { 1,2,3,4,5,6,7,8,9 } - { 5,6,7,8,9 }

= { 1,2,3,4 }

= A

Therefore ,

( A' )' = A

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