Question

the boolean expression (p^q)v ((-q)v p) is equivalent to:

Answer 1

$$\begin{gathered} \wedge s\tan dsfor\text{'}and\text{'}.Inbooleanalgebra\text{'}and\text{'}isexpressedby\text{'}.\text{'} \\ \vee s\tan dsfor\text{'}or\text{'}.Inbooleanalgebra\text{'}or\text{'}isexpressedby\text{'}+\text{'} \\ Inbooleanlagebranegativeofastatementisrepresentedbyitscomplementi.e.-\left(q\right)\to \overline{q} \\ Sothestatement\left(p\wedge q\right)\vee \left(-\left(q\right)\vee p\right)isequivalentto\left(p.q\right)+\left(\overline{q}+p\right) \\ p.q+\overline{q}+p \\ \iff p.q+p+\overline{q} \\ \iff p.\left(q+1\right)+\overline{q} \\ \left\{Sinceq+1=1\right\} \\ \iff p+\overline{q} \end{gathered}$$