I am trouble understanding first three lines of proof . For onto we have to show that there exists some element in P(A) which doesnot have its preimage .But how did they have shown here
2026-04-07 16:10:25.1775578225
To show function is not surjective
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First three lines is restating what we have to show. The problem I see is notation because author uses same name $B$ for the set in $A$ and as an element in $P(A)$. We don't have surjectivity when we can find an element which doesn't have inverse. Author in the first three lines just says that he will construct this set/element in $P(A)$ and names it $B$.