To demonstrate the logical equivalence of the statements p v (q ^ r) and (p v q) ^ (p v r) using a truth table, one must fill out the truth values for all combinations of p, q, and r. The truth table shows that both expressions yield identical results across all scenarios, confirming their equivalence. In contrast, the expression (p v q) ^ r does not match the truth values of the first two statements, indicating that it is not logically equivalent. Venn diagrams can also illustrate these relationships visually, highlighting the overlaps and distinctions between the sets represented by the statements. This analysis effectively verifies logical equivalence through both truth tables and Venn diagrams.
