Question

If A = {1} and phi is null set .Find
(a) P (P(A))
(b) P(P(P(phi)))

correct answer as brainliast​

Answer 1

Answer:

Step-by-step explanation:

The powerset of an infinite ordinal gives the next largest infinite ordinal.

It is the set containing the null set.

Since the powerset is the set of all subsets, and the empty set contains no elements, its only subset is the empty set.

$0$

$P(0)={0}$

$P({0})={0,{0}}$

$P({0,{0}})={0,{0},{{0}},{0,{0}}}$

and so on.

These are sets of the size $2^n$, are the finite ordinals of the Von Neumann Universe. The powerset operation is used to climb up the latter.

Taken together (the union of all these sets), they give aleph null — countable infinity — the smallest infinite ordinal.

The powerset of aleph null gives the the second infinite ordinal. This ordinal has the cardinality (size) of the real numbers.

The finite and finite ordinals taken together form the Von Neumann Universe.

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