Tutorial 9

1

1. Transform $\neg P\to (\neg Q\wedge R)$

$$\begin{array}{rl}\neg P& \to (\neg Q\wedge R)\\ \neg \neg P& \vee (\neg Q\wedge R)\\ P& \vee (\neg Q\wedge R)\\ (P\vee \neg Q)& \wedge (P\vee R)\end{array}$$

Definite rule: $P\vee \neg Q\to P\vee R$. 2. Transform $\neg (S\vee R)\wedge T$

$$\begin{array}{rl}\neg (S\vee R)& \wedge T\\ \neg S\wedge \neg R& \wedge T\end{array}$$

Definite rule: $S\vee R\to T$.

2

1. Transform $Q\wedge (\neg W\to \neg (R\wedge T))$.

$$\begin{array}{rl}Q& \wedge (\neg W\to \neg (R\wedge T))\\ Q& \wedge (\neg \neg W\vee \neg (R\wedge T))\\ Q& \wedge (W\vee \neg (R\wedge T))\\ Q& \wedge (W\vee \neg R\vee \neg T)\end{array}$$

Definite rule: $W\vee \neg R\vee \neg T\to Q$. 2. Transform $\neg (R\to \neg T)$.

$$\begin{array}{rl}& \neg (R\to \neg T)\\ & \neg (\neg R\vee \neg T)\\ \neg \neg R& \wedge \neg \neg T\\ R& \wedge T\end{array}$$

stuck.

2b

$$//$$

3

$$S,R,P\models \mathcal{P}$$