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\newcommand{\question}[1]{\stepcounter{qnum}\bigskip\noindent{\bf \arabic{qnum}. #1}}  \newcommand{\rand}{\textsf{R}}  \newcommand{\E}{\mathop{\textrm{E}}}  \newcommand{\np}{\textsf{NP}}  \question{Fool me once\dots} Define the function $f_{\textsf{MAJ}} :  \{0,1\}^n \times \{0,1\}^n \to \{0,1\}$ to return $1$ iff at least  $n+1$ bits of its input are 1. Give a fooling set of size $n$ for  $f_{\textsf{MAJ}}$.  \vfill