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0 stands for the empty set
Let P(X) denote the power set of the set X. FindP(P(P(P(0))))
0 stands for the empty set
Let P(X) denote the power set of the set X. FindP(P(P(P(0))))
Solution
I will use to denote the empty set.
P()={} (note that this is also denoted by 1 inaxiomatic set theory)
P(P())=P({})={,{}}
P(P(P()))=P({,{}})={,{},{{}},{,{}}}
P(P(P(P())))=P({,{},{{}},{,{}}})={{,{},{{}},{,{}}},{,{},{{}}},{,{},{,{}}},{{},{{}},{,{}}},{{
{}},{,{}}},{{},{{}}},{{},{,{}}},{,{}},{,{{}}},{,{,{}}},,{},{{}},{{{}}},{{,{}}}}
The last set contains 16 elements. You might want to work themout this way: Call A to be , B to
be {}, C to be{{}} and D to be {,{}}. Now write down allsubsets of {A,B,C,D}.

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0 stands for the empty setLet P(X) denote the power set of the s.pdf

  • 1. 0 stands for the empty set Let P(X) denote the power set of the set X. FindP(P(P(P(0)))) 0 stands for the empty set Let P(X) denote the power set of the set X. FindP(P(P(P(0)))) Solution I will use to denote the empty set. P()={} (note that this is also denoted by 1 inaxiomatic set theory) P(P())=P({})={,{}} P(P(P()))=P({,{}})={,{},{{}},{,{}}} P(P(P(P())))=P({,{},{{}},{,{}}})={{,{},{{}},{,{}}},{,{},{{}}},{,{},{,{}}},{{},{{}},{,{}}},{{ {}},{,{}}},{{},{{}}},{{},{,{}}},{,{}},{,{{}}},{,{,{}}},,{},{{}},{{{}}},{{,{}}}} The last set contains 16 elements. You might want to work themout this way: Call A to be , B to be {}, C to be{{}} and D to be {,{}}. Now write down allsubsets of {A,B,C,D}.