diff --git a/hw2/while-semantics.pdf b/hw2/while-semantics.pdf
index d97dae0..fb59f46 100644
Binary files a/hw2/while-semantics.pdf and b/hw2/while-semantics.pdf differ
diff --git a/hw2/while-semantics.tex b/hw2/while-semantics.tex
index 31c9993..fe6f600 100644
--- a/hw2/while-semantics.tex
+++ b/hw2/while-semantics.tex
@@ -43,6 +43,7 @@ you will implement the semantics for a small imperative language, named WHILE.
 \newcommand{\whilee}[2]{\mbox{\tt while}~(#1)~#2}
 \newcommand{\true}{\mbox{\tt true}}
 \newcommand{\false}{\mbox{\tt false}}
+\newcommand{\note}[1]{\mbox{\tt not}~{#1}}
 
 \begin{figure}\label{fig:lang}
 \caption{The WHILE language}
@@ -56,12 +57,16 @@ you will implement the semantics for a small imperative language, named WHILE.
   \mydefcase{e ~op~ e}{binary operations}
   \mydefcase{\ife e e e}{conditional expressions}
   \mydefcase{\whilee e e}{while expressions}
+  \mydefcase{e ~boolop~ e}{boolean binary operations}
+  \mydefcase{\not e}{negation}
   \\
   \mydefhead{v ::=\qquad\qquad\qquad\qquad}{Values}
   \mydefcase{i}{integer values}
   \mydefcase{b}{boolean values}
   \\
   op ::= & + ~|~ - ~|~ * ~|~ / ~|~ > ~|~ >= ~|~ < ~|~ <=  & \mbox{\emph{Binary operators}} \\
+  \\
+  boolop ::= & and ~|~ or  & \mbox{\emph{Boolean binary operators}} \\
 \end{array}
 \]
 \end{figure}
@@ -366,6 +371,18 @@ Finally, implement the interpreter to match your semantics.
 % }{
 %   \bstep{\whilee{e_1}{e_2}}{\sigma}{\ife{v_1}{e_2;\whilee{e_1}{e_2}}{\false}}{\sigma''}
 % }
+\bsrule{B-Not}{
+  \bstep{e}{\sigma}{b}{\sigma'}
+}{
+  \bstep{\note{e}}{\sigma}{\neg b}{\sigma'}
+}
+\bsrule{B-BoolOp}{
+  \bstep{e_1}{\sigma}{b_1}{\sigma'} \\
+  \bstep{e_2}{\sigma'}{b_2}{\sigma''} \\
+  b = apply(boolop, b_1, b_2)
+}{
+  \bstep{e_1~boolop~e_2}{\sigma}{b}{\sigma''}
+}
 \end{array}
 \]
 \end{figure}