# Set theory construction

What is N(U(P(2)-2)?

where N is the intersection of, U is the union of, and P(A) is the power set of A,and the minus sign represents relative complement or set difference

I get 0, Exercises in Set Theory by L.E. Sigler (Ex. 1.23) gives 1 - I reason as follows:

P(2) = {0,1,2, {1}}

P(2) - 2 = {0,1,2, {1}} - {0,1} = {2, {1}}

U((P(2)-2) = U({2, {1}} = { {0,1}, {1}} = {0,1} = 2

N2 = N{0,1} = 0

Am I missing something?

-

You correctly calculated $\wp(2)\setminus 2$ as $\big\{2,\{1\}\big\}$. There’s an error in your calculation of $\bigcup\big(\wp(2)\setminus 2\big)$, a missing $\bigcup$, but I think that it’s just a typo: you should have
$$\bigcup\big(\wp(2)\setminus 2\big)=\bigcup\big\{2,\{1\}\big\}=\bigcup\big\{\{0,1\},\{1\}\big\}=\{0,1\}=2\;.$$
$$\bigcap 2=\bigcap\{0,1\}=0\;.$$