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

#1**+1 **

The "complement" of a set just means all the elements of the universal set,* U*, that

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 { }

And that's the final answer

CPhill
May 20, 2017