Logic Operators in Discrete Mathematics

Understand how logical operators work in mathematics and computing: AND, OR, NOT, Implies, IFF, and XOR.

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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.

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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.

🧠 Quick Quiz: Test Your Logic Knowledge

1. When is the AND operator (∧) true?



2. What does the OR operator (v) evaluate to when one operand is true?



3. What is the result of ¬p when p is true?



4. When is p → q false?



5. What condition makes p ↔ q true?



6. When is the XOR operator (⊕) true?



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