Solution

The correct answer is Option 2.

Key Points

• The Boolean identities match as follows:
• A. Domination law (I): x + 1 = 1
• B. Associative law (IV): x + (y + z) = (x + y) + z
• C. Distributive law (II): x + (yz) = (x + y)(x + z)
• D. Absorption law (III): x + xy = x
• The correct matching of LIST-I with LIST-II is: A-I, B-IV, C-II, D-III.
• This matches the answer provided in Option 2.

Additional Information

• Boolean laws and identities:
  • Domination law: Represents the principle that any variable ORed with 1 results in 1 (x + 1 = 1).
  • Associative law: Indicates that the grouping of variables in an OR or AND operation does not affect the result (x + (y + z) = (x + y) + z).
  • Distributive law: Provides a way to distribute OR over AND or vice versa (x + (yz) = (x + y)(x + z)).
  • Absorption law: Simplifies expressions by absorbing redundant terms (x + xy = x).
• Applications of Boolean identities:
  • Used in digital circuit design and simplification of logic circuits.
  • Help in minimizing the number of logic gates required, thereby optimizing circuit design.
  • Play a critical role in computer science, particularly in database query optimization and programming logic.
• Importance of Option 2:
  • Option 2 provides the correct mapping of Boolean laws with their respective identities.
  • Ensures clarity and understanding of how these laws function in Boolean algebra.