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 26: Simplify the Boolean expression (A + B)(A' + C).

Solution: AC + A'B

Using the Distributive Law: (A + B)(A' + C) = AA' + AC + BA' + BC.
Simplifying: 0 + AC + A'B = AC + A'B.

Question 27: Simplify the Boolean expression A + A'B'.

Solution: A + B'

Using the Distributive Law: A + A'B' = A + B'.

Question 28: Simplify the Boolean expression A'B + AB'.

Solution: A ⊕ B

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

Question 29: Prove that A * A' = 0.

Solution: 0

This is the Complement Law in Boolean algebra: A * A' = 0, as a variable ANDed with its complement is always 0.

Question 30: Prove that A + A' = 1.

Solution: 1

This is the Complement Law in Boolean algebra: A + A' = 1, as a variable ORed with its complement is always 1.

Question 31: Simplify the Boolean expression A + AB + A'B'.

Solution: A + B'

Using the Distributive Law: A + AB + A'B' = A + B'.

Question 32: Simplify the Boolean expression A'B + A'B'.

Solution: A'

Using the Distributive Law: A'B + A'B' = A'(B + B').
Since B + B' = 1, the expression simplifies to A'.

Question 33: Simplify the Boolean expression AB + AB'.

Solution: A

Using the Distributive Law: AB + AB' = A(B + B').
Since B + B' = 1, the expression simplifies to A.

Question 34: Simplify the Boolean expression A(A' + B)(A + B').

Solution: AB'

Using the Distributive Law: A(A' + B)(A + B') = A(A + B')(A' + B).
Simplifying: A(A + B')(A' + B) = A * AB' = AB'.

Question 35: Simplify the Boolean expression A'B' + AB + A'B.

Solution: B + A'

Group terms: (A'B' + A'B) + AB = A'(B' + B) + AB = A' + AB.
Using Absorption Law: A' + AB = A' + B.

Question 36: Simplify the Boolean expression (A + B')(A' + B').

Solution: B'

Using the Distributive Law: (A + B')(A' + B') = A(A' + B') + B'(A' + B').
Simplifying: A'B' + A'B = A' + B'.

Question 37: Simplify the Boolean expression A(B + C') + A'B.

Solution: B + AC'

Using the Distributive Law: A(B + C') + A'B = AB + AC' + A'B.
Group terms: (AB + A'B) + AC' = B(A + A') + AC'.
Simplifying: B + AC'.

Question 38: Simplify the Boolean expression A + (A'B)' + A'C.

Solution: A + B + C

Using De Morgan's Law: A + (A'B)' = A + A + B = A + B.
Thus, A + B + A'C simplifies to A + B + C.

Question 39: Simplify the Boolean expression A + A'B + A'B'.

Solution: A + B'

Group terms: A + A'B + A'B' = A + A'(B + B').
Since B + B' = 1, the expression simplifies to A + A' = A.

Question 40: Simplify the Boolean expression (A + B)(A' + B).

Solution: A + B

Using the Distributive Law: (A + B)(A' + B) = AA' + AB + A'B + BB.
Simplifying: 0 + AB + A'B + B = A + B.

Question 41: Simplify the Boolean expression (A + B')(A + C').

Solution: A + B'C'

Using the Distributive Law: (A + B')(A + C') = A(A + C') + B'(A + C').
Simplifying: A + B'C'.