Boolean Algebra Questions

here, 53 question are given for pratice boolean algebra

These questions are generally asked in university exam

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Question 14: Simplify the Boolean expression A + A.

Solution: A

This is the Idempotent Law of Boolean algebra, which states that A + A = A.

Question 15: Simplify the Boolean expression A + 1.

Solution: 1

This follows the Domination Law: A + 1 = 1, because any variable ORed with 1 is always equal to 1.

Question 16: Simplify the Boolean expression A * 0.

Solution: 0

This follows the Domination Law: A * 0 = 0, because any variable ANDed with 0 is always equal to 0.

Question 17: Simplify the Boolean expression A * 1.

Solution: A

This follows the Identity Law: A * 1 = A, because any variable ANDed with 1 remains unchanged.

Question 18: Prove that A * A = A.

Solution: A

This is the Idempotent Law of Boolean algebra, which states that A * A = A.

Question 19: Simplify the Boolean expression (A + B)'.

Solution: A'B'

This is an application of De Morgan's Law: (A + B)' = A'B'.

Question 20: Simplify the Boolean expression (AB)'.

Solution: A' + B'

This is an application of De Morgan's Law: (AB)' = A' + B'.

Question 21: Simplify the Boolean expression A(A' + B).

Solution: AB

Using the Distributive Law: A(A' + B) = AA' + AB.
Since AA' = 0, the expression simplifies to AB.

Question 22: Simplify the Boolean expression AB + A'B'.

Solution: A ≡ B (A XNOR B)

This is the standard expression for XNOR (exclusive NOR): A ≡ B = AB + A'B'.

Question 23: Simplify the Boolean expression (A + B')(A' + B).

Solution: A'B + AB'

This is the expression for XOR: A'B + AB' = A ⊕ B.

Question 24: Simplify the Boolean expression (A' + B)(A' + B').

Solution: A'

Using the Distributive Law: (A' + B)(A' + B') = A'(A' + B') + B(A' + B').
Simplifying: A' + B(A' + B') = A' + B'A + B'.
Using De Morgan's, the final result is A'.

Question 25: Simplify the Boolean expression A(B + C).

Solution: AB + AC

This follows the Distributive Law: A(B + C) = AB + AC.