(1) A INTERSECTION {A}

A may have many elements, but none of which is A itself.
A set is NEVER an element of itself.

However,

{A} has just one element, A.

Therefore A and {A} have NO ELEMENTS in common!  Therefore
their intersection is empty.

Answer: the empty set.

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 {A,{A}}-A

We remove A from the set and that leaves {{A}},
it must have two braces on each side of A.

That is the set that contains as its only element
the set that contains A as its only element.

Answer {{A}}

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Edwin