Question

Use truth tables to verify the commutative laws.

(a)$\text{p}\vee \text{q}\equiv \text{q}\vee \text{p}$(b)$\text{p}\wedge \text{q}\equiv \text{q}\wedge \text{p}$

Short answer

The given commutative laws can be verified using truth tables. Prepare the truth table for every statement and also take different values of p and q such as every possible combination of T and F to check the result for their verification.

Step-by-step solution

 Step1: 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.

Verification of Commutative laws using Truth Tables

(a)$\text{p}\vee \text{q}\equiv \text{q}\vee \text{p}$

Check the outcomes of $\text{p}\vee and\text{q}\vee \text{p}$

From the truth tables, it is observed that $\text{p}\vee \text{q}\equiv \text{q}\vee \text{p}$as their outcomes are the same.

(b) $\text{p}\wedge \text{q}\equiv \text{q}\wedge \text{p}$

Prepare a truth table for$\text{p}\wedge \text{q}$

Make a truth table for $\text{q}\wedge \text{p}$

Truth Table

Check the outcomes of $\text{p}\vee \text{qandq}\vee \text{p}$

From the truth tables, it is observed that $\text{p}\wedge \text{q}\equiv \text{q}\wedge \text{p}$ as their outcomes are the same.

Therefore, the commutative laws have been verified using truth tables.