How many elements must a set have if the number of proper subsets of the set is one half of the total number of subsets of the
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For 
to be continuous at 
, we need to have
Note that
means that 
, but that 
is *approaching* 5. We're told that for , we have
We can write
and the limit would be
and so is discontinuous.
Note that
We can write
and the limit would be
and so
From trigonometry we know that:
if
then, (where
is an integer)
This can be rewritten in degrees as:
.............(Equation 1)
Now, in our case,
Therefore, (Equation 1) can be written as:
..........(Equation 2)
Now, to find the correct options all that we have to do is replace n by relevant integers and find the values of that match.
For n=2, (Equation 2) gives us: .
Thus,
Now, we know that:
Let n=-1, then:
Thus,
Likewise,
Only the last option will never match
because no integral value of
will ever give
Thus the last option is the correct option.