qwer: 8

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Arjun asked in Algorithms Apr 3

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Which of the following is/are true?

If $S$ is a set and $|S| = 103$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.
If $S$ is a set and $|S| = 103$, then $S$ is a power set of some set (that is, there is some set $T$ where $S = \mathcal{P}(T))$.
If $S$ is a set and $|S| = 8$, then $S$ is a power set of some set (that is, there is some set $T$ where $S = \mathcal{P}(T))$.
If $S$ is a set and $|S| = 8$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.

Arjun asked in Algorithms Apr 3

by Arjun

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1 Answer

Arjun · Answer 1 · 2024-04-03T04:29:49+0000

For Option C:
Counterexample: $S = \{1, 2, \dots, 8 \}$, here $S$ is Not a powerset of any set T.