1. **Stating the problem:** We want to determine when two or more propositions are logically equivalent. 2. **Definition:** Two propositions $P$ and $Q$ are logically equivalent if they have the same truth value in every possible scenario. 3. **Formula:** Logical equivalence is denoted as $P \equiv Q$ and means $P \leftrightarrow Q$ is a tautology (always true). 4. **Method 1 - Truth Tables:** Construct truth tables for each proposition and compare their truth values row by row. If all corresponding truth values match, the propositions are logically equivalent. 5. **Method 2 - Logical Laws:** Use known logical equivalences and laws (like De Morgan's laws, distributive laws, etc.) to transform one proposition into the other. 6. **Example:** Suppose $P = \neg (A \wedge B)$ and $Q = \neg A \vee \neg B$. Using De Morgan's law, $\neg (A \wedge B) \equiv \neg A \vee \neg B$, so $P$ and $Q$ are logically equivalent. 7. **Summary:** To know if propositions are logically equivalent, either verify their truth tables match or use logical equivalences to transform one into the other.