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Other input terms : A union B, A intersect B, A', P(A), A - B, A delta B, A cross B, |A|, 1 belongsto A, A subset B, (A union B)' = A' intersect B'
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Find A={x<=5, x in N}, B={2<=x<=8, x in N}, U={1<=x<=10, x in N}, find (A union B)' = A' intersect B'

Solution:
Your problem `->` A={x<=5, x in N}, B={2<=x<=8, x in N}, U={1<=x<=10, x in N}, find (A union B)' = A' intersect B'


`U={1<=x<=10, x in n}`
`:.U={1,2,3,4,5,6,7,8,9,10}`

`A={x<=5, x in n}`
`:.A={1,2,3,4,5}`

`B={2<=x<=8, x in n}`
`:.B={2,3,4,5,6,7,8}`

To find LHS = `(A uu B)'`

`A uu B = {1,2,3,4,5} uu {2,3,4,5,6,7,8}`

`= {1,color{red}{2},color{green}{3},color{blue}{4},color{maroon}{5}} uu {color{red}{2},color{green}{3},color{blue}{4},color{maroon}{5},6,7,8}`

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

`(A uu B)' = {1,2,3,4,5,6,7,8}'`

`= {9,10}`

`:. (A uu B)' = {9,10} ->(1)`

To find RHS = `A' ∩ B'`

`A' = {1,2,3,4,5}'`

`= {6,7,8,9,10}`

`B' = {2,3,4,5,6,7,8}'`

`= {1,9,10}`

`A' nn B' = {6,7,8,9,10} nn {1,9,10}`

`= {6,7,8,color{red}{9},color{green}{10}} nn {1,color{red}{9},color{green}{10}}`

`= {9,10}`

`:. A' ∩ B' = {9,10} ->(2)`

From (1) and (2)
`:. (A uu B)' = A' ∩ B'`






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