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\paragraph{Problem 2 (18 points)}
Show that there is no universal hardcore bit.
In more detail, show that for every $n\in\mathbb{N}$, there is no deterministic function $h: \{0,1\}^n \to \{0,1\}$ such that for any polynomial $p()$, \emph{any} one-way function $f: \{0,1\}^n \to \{0,1\}^{p(n)}$, $h$ is a hardcore bit for $f$. |