Is set of empty set is a subset of empty set?

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Is {∅} ⊆ ∅ true?

I don't think so, because If ∅ is a subset of every set (also ∅) ∅ ⊆ A it means that no elements are a part of any set, but in this case {∅} ⊆ ∅ must be true if every element in A is an element in B, B is just an empty set that not contains elements.

Am I right? Thanks

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It is not true.

"I don't think so..."

So the outcome of your thinking on this is correct. Unfortunately I have troubles in following the thinking itself expressed in your question, and the fact that it is quite a story makes me suspicuous.

More concise you can say: $\{\varnothing\}$ has an element, and if $\{\varnothing\}\subseteq\varnothing$ is true then this element will also be an element of $\varnothing$.

This however is absurd, since by definition $\varnothing$ has no elements. We conclude that $\{\varnothing\}\subseteq\varnothing$ is false.