SOLUTION: Let Universal Set = {a, b, c, d, e, f}, A = {d, e, f}, and B = {a, b, c, f}. Find each specified set. (A ⋃ B)'=

                  (A ⋃ B)'

       ({d, e, f} ⋃ {a, b, c, f})'

⋃, union, means to put the sets together then take out any 
duplications:

We put them together:

({d, e, f, a, b, c, f})'

Then we take out the duplications:

({d, e, f, a, b, c})'

The ' mark means "the complement". That means to remove the set 
from the universal set and put the rest in a set:

So we remove {d, e, f, a, b, c} from the universal
set {a, b, c, d, e, f}, 

and we don't have anything left.  Therefore we put nothing
at all inside braces and the answer is the empty set:

          { }

But some people don't like that and think it ought to look
more like the number zero.  It can't be zero because zero 
is a number not a set so they write this:

          ∅

Edwin