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Just getting into set theory just had a few questions/clarifications I guess you could call it.

if X = {Ø, a} Y={{Ø}, a} and Z = {a, {a}, {Ø}}

So i understand X has 2 elements along with Y and Z has 3.

I know what the cardinalities are of basic sets like {2, 3, 4, 5} etc but how do they apply to sets such as the above?

On top of this if U = Z - X

thats {a, {a}, {Ø}} - {Ø, a} does U = {{a}}? I am just unsure when there is a set as an element such as {Ø} do the same rules apply?

Cheers in advance,

Sim