Question

Show that$\mathbf{\text{p}}\mathbf{|}\mathbf{\text{q}}$is logically equivalent to$\neg (\text{p}\wedge \text{q})$.

Short answer

For showing,$\text{p}|\text{q}$and $\neg (\text{p}\wedge \text{q})$equivalent, prepare the truth table for every statement and also take different values of p and q such as every possible combination of and Fto check the result for their verification.

Step-by-step solution

Definition of Truth Table

A logic gate truth tabledepicts each feasible input sequence to the gate or circuit, as well as the resulting output based on the combination of these inputs.

To show and are logically equivalent

Take two variables as inputs such as P and q.

p NANDis denoted by$\text{p}|\text{q}$.

Prepare the truth table for$\text{p}|\text{q}$ and$\neg (\text{p}\wedge \text{q})$

Truth Table

Check the outcomes of$\text{p}|\text{q}$ and.$\neg (\text{p}\wedge \text{q})$

From the truth tables, it is observed that $\text{p}|q\equiv \neg (\text{p}\wedge \text{q})$as their outcomesare the same.

Therefore, it has been proved that$\text{p}|\text{q}$ is logically equivalent to$\neg (\text{p}\wedge \text{q})$.