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Determine whether $(\sim q \wedge (p \rightarrow q)) \rightarrow \sim p$
asked in Mathematical Logic by Boss (10.5k points) | 20 views

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$(\sim p \wedge (p \rightarrow q)) \rightarrow \sim p$

We know that $p \rightarrow q \equiv \sim p\vee q$

$(\sim p \wedge (\sim p\vee q)) \rightarrow \sim p$

Convert $\wedge\equiv\cdot ,\vee\equiv +$

Now,   $\overline{p}.(\overline{p}+q)\rightarrow \overline{p}$

        $(\overline{p}.\overline{p}+\overline{p}.q)\rightarrow \overline{p}$

        $(\overline{p}+\overline{p}.q)\rightarrow \overline{p}$

       $\overline{p}\rightarrow \overline{p}$

       $\overline{\overline{p}}+\overline{p}$

      $p+\overline{p}=\overline{p}+p=1$

Now we can write    $p \vee \sim p\equiv \sim q\vee p\equiv T$

  So, this is Tautology.
answered by Boss (34.3k points)
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It is tautology.

answered by Boss (33.4k points)
0
In step 3: q`p` ->p`

In step 4:(q`p`)`+p` instead of  implication symbol

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