Help -Negate statement then reexpress as equiv positive statement

[IntroAnalysis]

Homework Statement

$\forall$a $\in$A$\exists$b$\in$B(a$\in$C $\leftrightarrow$ b$\in$C).

Homework Equations

The Attempt at a Solution

\forall

This is equivalent to $\exists$a$\in$A$\neg\exists$b$\in$B(a$\in$C $\leftrightarrow$b$\in$C).

Homework Statement

 

[4189]

The first part of your solution appears correct however you still need to negate that which is in the parantheses. It may help to write out the logical operators in words to give you a better picture of the question. I came up with a solution, but I will wait to post till you give the rest of your problem a shot.