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Prove the following properties of Boolean algebras. Give a reason for each step. a. x +
Chapter 8, Problem 9(choose chapter or problem)
Prove the following properties of Boolean algebras. Give a reason for each step. a. x + (x # y) = x (absorption properties) x # (x + y) = x b. x # 3 y + (x # z)4 = (x # y) + (x # z) (modular properties) x + 3 y # (x + z)4 = (x + y) # (x + z) c. (x + y) # (x + y) = y (x # y) + (x # y) = y d. (x + (y # z)) = x # y + x # z (x # (y + z)) = (x + y) # (x + z) e. (x + y) # (x + 1) = x + (x # y) + y (x # y) + (x # 0) = x # (x + y) # y
Questions & Answers
QUESTION:
Prove the following properties of Boolean algebras. Give a reason for each step. a. x + (x # y) = x (absorption properties) x # (x + y) = x b. x # 3 y + (x # z)4 = (x # y) + (x # z) (modular properties) x + 3 y # (x + z)4 = (x + y) # (x + z) c. (x + y) # (x + y) = y (x # y) + (x # y) = y d. (x + (y # z)) = x # y + x # z (x # (y + z)) = (x + y) # (x + z) e. (x + y) # (x + 1) = x + (x # y) + y (x # y) + (x # 0) = x # (x + y) # y
ANSWER:Step 1 of 11
Boolean algebra is used to analyze gates and circuits. It is used to perform mathematical operations on binary numbers. The basic operators on Boolean algebra are AND, OR, and NOT.