I'm practicing for an exam coming up and I want to make sure I understand power sets. I've answered this question and I was hoping someone could tell me if my answer is correct.

Let A be the set that has the three elements { }, 1, and {2, 3}. What are the 
eight elements of set PS(A) of set A.

Answer: [{{}}, {1}, {2, 3}, {{}, 1}, {{}, {2, 3}}, {1, {2, 3}}, {{}, {1}, {2, 3}}, {}]

Is having a set of the empty set the correct way to go about this? Thanks!

  • $\begingroup$ It may help your notation to indicate the empty set as $\emptyset$ rather than $\{\}$. Cleans things up. (The command is \emptyset ) $\endgroup$
    – Alan
    Dec 2, 2014 at 4:19

1 Answer 1


Yes, you are correct. You can just take any three element set, form its power set, then substitute the elements of the set you are given. The empty set is an element like any other, which seems to be the purpose of the exercise.


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