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

Solution: A + B

Expanding: A(B + C) + B(A + C') = AB + AC + BA + BC' = AB + AC + BC'.
Using Absorption: AB + AC + BC' = A + B.

Question 43: Simplify the Boolean expression A'BC + AB'C + ABC'.

Solution: BC + AC'

Group terms: A'BC + AB'C + ABC' = (A'B + AB')C + AC'.
Using XOR: (A'B + AB')C = C.
Thus, the result is BC + AC'.

Question 44: Simplify the Boolean expression AB'C + A'BC'.

Solution: A'BC' + AB'C

This expression is in its simplest form and represents exclusive OR of multiple terms.

Question 45: Simplify the Boolean expression A + A'B + A'C.

Solution: A + B + C

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

Question 46: Simplify the Boolean expression A'B + AB' + AB.

Solution: A + B

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

Question 47: Simplify the Boolean expression A(B + C) + B(A + C).

Solution: A + B

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

Question 48: Simplify the Boolean expression (A + B)(A' + C).

Solution: AC + A'B

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

Question 49: Simplify the Boolean expression A'B'C + A'BC' + ABC.

Solution: A'C + BC

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

Question 50: Simplify the Boolean expression A + A'BC.

Solution: A + BC

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

Question 51: Simplify the Boolean expression A'B' + AB + A'B.

Solution: A' + B

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

Question 52: Simplify the Boolean expression A + A'B + B'C'.

Solution: A + B'C'

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

Question 53: Simplify the Boolean expression A + B(A' + C).

Solution: A + BC

Using the Distributive Law: A + B(A' + C) = A + BA' + BC.
Using Absorption: A + BA' + BC = A + BC.