We need to understand the concept of logical equivalence to better understand the laws or propositional logic.

## What is a Tautology and a Contradiction in Logic?

In logic, a tautology occurs when a compound proposition is always true, and a contradiction occurs when a compound proposition is always false.

In English, tautology is saying the same thing using different words.

**Example of tautology and contradiction in logic**

S ∨ ¬S is a tautology because the value is always true.

S ∧ ¬S is a contradiction because the value is always false.

## What Are Logically Equivalent Compound Propositions?

When two compound propositions have the same value, they are considered logically equivalent. This symbol ≡ indicates that

Q ≡ Q is logically equivalent regardless of their inner statements’ value.

**Example of logically equivalent compound propositions**`R →¬R ≡¬R`

both sides are logically equivalent`T →¬T ≡¬T`

assuming R = True`T →¬F ≡¬T`

first negation evaluates to False`T →¬F ≡¬F`

second negation evaluates to False`F ≡¬F`

the logical proposition evaluates to false because the hypothesis is True while the conclusion is False`F ≡¬F`

both statements are logically equivalent