Let's say we have a set A = {1, 2, 3, 4}

I understand that, for example, $\displaystyle \left\{{2, 3}\right\}\in P(A)$, but why is it that$\displaystyle \left\{{\varnothing}\right\}\subseteq P(A)$?

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- Nov 17th 2011, 04:18 PMRobinatorQuick question about the empty set and the power set
Let's say we have a set A = {1, 2, 3, 4}

I understand that, for example, $\displaystyle \left\{{2, 3}\right\}\in P(A)$, but why is it that$\displaystyle \left\{{\varnothing}\right\}\subseteq P(A)$? - Nov 17th 2011, 04:26 PMTheChazRe: Quick question about the empty set and the power set
Take a subset S of A.

Then this subset is an element of P(A).

S is in P(A)

For a set to be a subset of P(A), each of its elements must be in P(A).

Ie each of its elements must be a subset of A.

The empty set is a subset of A.

The set containing the empty set is therefore a subset of P(A) - Nov 17th 2011, 04:34 PMRobinatorRe: Quick question about the empty set and the power set
So if I took the set {{2, 3}} it becomes a subset of P(A) rather than an element, correct? I think I understand, thank you.

- Nov 18th 2011, 07:37 AMMoeBleeRe: Quick question about the empty set and the power set
- Nov 18th 2011, 07:40 AMMoeBleeRe: Quick question about the empty set and the power set