Logical operators are core tools in propositional logic, used to build and evaluate logical statements. These operators allow you to express and analyze logical relationships effectively.
🔧 AND ( ∧ )
The "AND" operator is true only when both propositions are true. If p and q are both true, then p ∧ q is true.
🚪 OR ( v )
The "OR" operator is true if at least one operand is true. p v q is true when p is true, q is true, or both.
🚫 NOT ( ¬ )
The "NOT" operator reverses the truth value. ¬p is true if p is false, and vice versa.
➡️ Implies ( → )
The "implies" operator is false only when the first operand is true and the second is false. Otherwise, p → q is true.
🔁 If and only If ( ↔ )
This operator is true when both operands are either true or both are false. p ↔ q represents logical equivalence.
❌ Exclusive OR ( ⊕ )
The "XOR" operator is true when p and q have different truth values. p ⊕ q is true when one is true and the other is false.
💡 Tip: Logical operators are the foundation of proofs, circuits, and logic design in computer science.
