cant solve this problem (proof by contradiction)

**sub_2** · March 1st 2009, 01:55 PM

i tried to solve this question 100 times but could n't get the right answer
plz help guys

**Plato** · March 1st 2009, 02:42 PM

$\begin{array}{llr} 1 & {\left( {S \wedge R} \right) \to Q} & {} \\ 2 & {\neg R \to \neg P} & {} \\ 3 & {S \wedge P} & {} \\ 4 & {\neg Q} & {\text{assume}} \\ \end{array}$
$ \begin{array}{llr} 5 & {\neg \left( {S \wedge R} \right)} & {1,4} \\ 6 & {\neg S \vee \neg R} & 5 \\ 7 & S & 3 \\ 8 & {\neg R} & 6 \\ 9 & {\neg P} & {2,8} \\ {10} & P & 3 \\ {} & {P \wedge \neg P} & {8,9 \text{ contradiction}} \\ \end{array}$

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