ollowing formula as much as possible using a series of equivalence laws.                  B ∧ ((B ∧ C) → ¬A) ∧

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Simplify the following formula as much as possible using a series of equivalence laws.
                 B ∧ ((B ∧ C) → ¬A) ∧ (C ∨ B)

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Step 1

Here We can simplify the formula using the following equivalence laws:

  1. Distributive law: A ∧ (B ∨ C) ≡ (A ∧ B) ∨ (A ∧ C)
  2. De Morgan's law: ¬(A ∧ B) ≡ ¬A ∨ ¬B
  3. Double negation: ¬¬A ≡ A
  4. Contrapositive: A → B ≡ ¬B → ¬A
  5. Idempotence: A ∧ A ≡ A
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