Let $A$ and $B$ be two sets. Statement: There exists $x\in B$ such that $x\notin A.$
My Question: What is the negation of the above statement?
My Answer is: For every $x\in B,$ we have $x\in A,$ that is $B\subset A.$ Is this correct?
There exists $x\in B$ such that $x\notin A.$
logic
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Best Answer
Edit because the OP changed the question. This is an answer to the one asked.
The assertion you want to negate is the definition of "proper subset":
The negation is
General remark for this kind of question. I think it's much easier to understand both question and answer with words instead of symbols where possible.