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{\large CS 291}\\
Homework 2
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\begin{flushright}
Milo Minderbinder\\
mmm123@truman.edu
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\textbf{Section 6.3, problem 7e.}  Give a formal proof for each of the
following tautologies by using the CP rule and by using the IP rule at
least once in each proof.

Prove $ \neg(A \land B) \land (B \lor C) \land (C \rightarrow D) \rightarrow (A \rightarrow D)$ is a tautology.


\emph{Answer:} 

\begin{tabular}{p{.8cm}p{8.5cm}l}
1. & $\neg(A \land B)$ & $P$ \\
2. & $B \lor C$ & $P$ \\
3. & $C \rightarrow D$ & $P$ \\
4. & \qquad $A$ & $P$ [for $A \rightarrow D$] \\
5. & \qquad\qquad $\neg D$ & $P$ [for $D$] \\
6. & \qquad\qquad $\neg C$ & 3,5,MT \\
7. & \qquad\qquad $B$ & 2,6,DS \\
8. & \qquad\qquad $A \land B$ & 4,7,Conj \\
9. & \qquad\qquad False & 1,8,Contr \\
10.& \qquad $D$ & 5-9,IP \\
11.& $A \rightarrow D$ & 4,10,CP\\
& QED & 1-3,11,CP\\
\end{tabular}

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