1. ## Power Set

Find the power set of each of the following sets.
a. 0
b. {0}
c. {0,{0}}

What is the cardinality of each of the power sets you just found?

Find the power set of each of the following sets.
a. $\emptyset$ b. $\{ \emptyset \}$ c. $\{ \emptyset, \{ \emptyset\}\}$
What is the cardinality of each of the power sets you just found?

If so, what do you think about the (a) part?

3. Originally Posted by captainjapan
Find the power set of each of the following sets.
a. 0
b. {0}
c. {0,{0}}

What is the cardinality of each of the power sets you just found?

Patrick Suppes in his book ,AXIOMATIC SET THEORY on page 47 gives a good proof of :

...........P(Φ) = { Φ }, Φ being the empty set.

After that we have that:

P({Φ}) = { Φ.{Φ}} AND :

P({φ,{Φ}}) = {Φ,{Φ},{{Φ}},{Φ,{Φ}}}

4. Yes that's my question. Sorry for the misunderstanding.

Find the power set of each of the following sets.
a. b. c.