Logical Equivalence and the Laws of Logic
Logical equivalence means that two propositional expressions have identical truth values under every assignment of their variables.
Summary
Logical equivalence means that two propositional expressions have identical truth values under every assignment of their variables. The notation holds exactly when is a tautology. Truth tables verify equivalence by comparing final columns, while logical laws establish it through valid symbolic rewrites.
Equivalent substitution preserves a formula's truth value, supporting Boolean condition simplification, assertion negation, and proofs of correctness for Boolean circuit transformations.
| Law | What changes | What is preserved |
|---|---|---|
| Commutative | Order of operands |
🧠 Key Concepts
- Logical equivalence
- Truth tables
- De Morgan's laws
- Implication law
- Commutative laws
- Associative laws
- Distributive laws
- Absorption laws
- Contraposition
- Tautologies and contradictions
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When checking two Boolean conditions with a truth table, what establishes their logical equivalence?
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Logical Equivalence and the Laws of Logic
📘 Overview Logical equivalence means that two propositional expressions have identical truth values under every assignment of their variables. Truth tables verify equivalence by comparing final columns; laws of logic establish equivalence through valid symbolic rewrites.
🧠 Key Idea The notation means that and express the same truth conditions. Replacing an expression with a logically equivalent expression preserves the truth value of the entire formula.
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Part of 🌱 BSCS Year 1 — Computing & College Foundations
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