Suppose you had three pieces of paper in a bag. One piece of paper has
13 written on it, one has 14 written on it, and one has 15 written on it."

You reach in the bag.  Then withdraw your hand. List all the possibilities
of what you could have in your hand when you draw it out:


Just list them all:

1. {13,14,15}  You could end up with all three pieces of paper in your hand.
2. (13,14}     You could end up with just the 13 and 14 in your hand with the
               15 still in the bag. 
3. (13,15}     You could end up with just the 13 and 15 in your hand with the
               14 still in the bag.
4. (14,15}     You could end up with just the 14 and 15 in your hand with the
               13 still in the bag.
5. (13}        You could end up with just the 13 in your hand with the
               14 and 15 still in the bag.
6. (14}        You could end up with just the 14 in your hand with the
               13 and 15 still in the bag.
7. (15}        You could end up with just the 15 in your hand with the
               13 and 14 still in the bag.
8. { }         You could end up with nothing in your hand with all three
               numbers still in the bag.

The formula is:  If there are N elements (members) in the set, the 
number of subsets is always .  So in the case where there are 3
elements (members) in the set, the number of subsets is .

When making a subset, there are always two choices for each element:
1. Put it in the subset.
2. Don't put it in the subset.

So when making a subset, you have exactly 2 choices with every element 
of the set.

You have those 2 choices for the 13, then those 2 choices for the 14, 
and finally those 2 choices for the 15.  So that's 2x2x2 = 8. 

Any way you do it, you get 8, which is answer (b) above.

Edwin