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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={3<=x<=7, x in N}, C={1<=x<=3, x in N}, find A union (B union C) = (A union B) union C

Solution:
Your problem `->` A={x<=5, x in N}, B={3<=x<=7, x in N}, C={1<=x<=3, x in N}, find A union (B union C) = (A union B) union C


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

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

`C={1<=x<=3, x in n}`
`:.C={1,2,3}`

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

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

`= {color{red}{3},4,5,6,7} uu {1,2,color{red}{3}}`

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

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

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

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

`:. A uu (B uu C) = {1,2,3,4,5,6,7} ->(1)`

To find RHS = `(A uu B) uu C`

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

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

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

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

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

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

`:. (A uu B) uu C = {1,2,3,4,5,6,7} ->(2)`

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






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