I'm sure this is an elementary question for most of you...

Let

Determine the following:

a) |A|

This one is easy; It's 3, because there are 3 objects in A.

b) |{A}|

I believe the cardinality here is 1, but I'm not sure...can someone explain WHY?

c) 2 ^ |A|

d) |2 ^ A |

I think c) and d) are asking the same thing but this seems tricky to me because the empty set is an element of A. Are c) and d) equal? If so, what are they and why?

e) Is the empty set an element of A?YES

f) Is the empty set a subset of A?YES

g) Is the set containing the empty set an element of A?????

h) Is the set containing the empty set a subset of A?????

I'm really trying to understand this so I'm looking for reasons WHY rather than just answers. Thanks for any input you can provide.