ข้อสอบ PAT 1 - มีนาคม 2557

$$\begin{gathered} \left(ก\right) \mathrm{จากโจทย์} \left(p\vee q\right)\leftrightarrow \left(r\wedge s\right)\equiv T \\ -\mathrm{แทน} p=T \\ \mathrm{จะได้} \left(T\vee q\right)\leftrightarrow \left(r\wedge s\right)\equiv T \\ \hspace{0.17em}\hspace{0.17em}T\leftrightarrow \left(r\wedge s\right)\equiv T\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathbf{\hspace{0.17em}}\mathbf{โดย} T\leftrightarrow T\equiv T \\ \mathrm{แสดงว่า} \therefore \left(r\wedge s\equiv T\right) \\ \mathrm{ดังนั้น} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}r, s \mathrm{ต้องจริงทั้งคู่} \mathrm{ข้อ} \left(ก\right) \mathrm{ถูก} \end{gathered}$$

$$\begin{gathered} \left(ข\right) \mathrm{จากโจทย์} \left(p\wedge q\right)\to \left(r\wedge s\right)\equiv [q \to (p \to r\left)\right]\wedge [p \to \left( q\to s\right)] \\ \mathrm{จัดรูปทั้งสองฝั่งให้เป็นรูปอย่างง่าย} \\ \mathrm{จะได้} \\ ~ \left(p\wedge q\right)\vee \left(r\wedge s\right)\equiv [~q \vee (~p \vee r\left)\right]\wedge [~p \vee \left( ~q\vee s\right)] \\ \left(~p\vee ~q\right)\vee \left(r\wedge s\right)\equiv [~q \vee ~p \vee r)]\wedge [~p \vee ~q\vee s] \\ \equiv [\left(~p \vee ~q\right) \vee r\left)\right]\wedge [\left(~p \vee ~q\right)\vee s] \\ \equiv [\left(~p \vee ~q\right)\vee \left[r\wedge s\right] \\ -\mathrm{ทั้งสองฝั่งสมมูลกัน} \mathrm{ข้อ} (ข) \mathrm{ถูก} \end{gathered}$$