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# Can you explain: Complements & Intersection & Union

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How do you solve a question like this?

If U={1,2,3,4,5,6,7,8,9,10,11,12}, and A={1,5,11,2}, B={3,4,5,8}, and C={2,7,8,9,10,11,12}, then find the complement of the union of the complement of A, the complement of B, and the complement of C.

Please give a step by step explanation

note: I don't understand any of this.

Thanks

Guest May 20, 2017
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The "complement" of a set just means all the elements of the universal set, U, that are not found in that set......so.....

The complement of A, denoted as A' =  { 2,3,4,6,7, 8, 9 ,10}

The complement of B  = B' = {1,2,6,7,9,10,11,12}

The complement of C  = C'  { 1,3,4,5,6 }

The  union of the complement of A, the complement of B, and the complement of C  means a listing of all the elements  in either A' ,B' or C'  or all three.

So  using the symbol U to denote union, we have

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

So....finally.......we want to find the complement of this last set......this means finding all of the elements in  the universal set  that are not contained in this set......notice that there are none.....so....the result of  this is called the empty set, denoted as  {    }