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# If A ⊆ B, is Ā ⊆ B (also with bar on top, dont know how to type it)?

(the b is also B with a line over it)

Basically, if A is a subset of B,

will not A always be a subset of not B?

### 1 Answer

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- Markus0003000Lv 710 years agoFavorite Answer
This is not true.

Say that A = ∅ (∅ is the empty set) and B = {1}.

Then Ā = {Everything in the universe} and B(bar) = {everything is the universe except 1}

Then A ⊆ B but Ā is not a subset of B(bar).

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