Question

The dual of the statement $\left[\mathrm{p}\vee \left(~\mathrm{q}\right)\right]\wedge \left(~\mathrm{p}\right)$ is

• A. $\text{p∨}\left(~\mathrm{q}\right)\vee ~\mathrm{q}$
• B. $\left(\mathrm{p}\wedge ~\mathrm{q}\right)\vee ~\mathrm{p}$
• C. $\mathrm{p}\wedge ~\left(\mathrm{q}\vee ~\mathrm{p}\right)$
• D. None of the above

Answer 1

The correct option is B

$\left(\mathrm{p}\wedge ~\mathrm{q}\right)\vee ~\mathrm{p}$

Finding the dual statement:

Given statement,

$\left[\mathrm{p}\vee \left(~\mathrm{q}\right)\right]\wedge \left(~\mathrm{p}\right)$

We know that, in duality, AND $\wedge$ is converted to OR $\vee$and OR $\vee$ is converted to AND $\wedge$.

Hence, $\left[\mathrm{p}\vee \left(~\mathrm{q}\right)\right]$ is converted to $\left[\mathrm{p}\wedge \left(~\mathrm{q}\right)\right]$ and $\wedge \left(~\mathrm{p}\right)$is converted to $\vee \left(~\mathrm{p}\right)$.

Therefore, the dual of the given statement is $\left(\mathrm{p}\wedge ~\mathrm{q}\right)\vee ~\mathrm{p}$.

Hence, option (B) is the correct answer