Boolean Algebra | Logic Simplification MCQs

1. The boolean expression $X=B+A\overline{B}+AB$ is equivalent to

1. A+B
2. $\overline{A}B$
3. $\overline{A+B}$
4. AB

2. The Boolean expression X = (A + B)(C + D) represents

1. two ORs ANDed together
2. two ANDs ORed together
3. A 4-input AND gate
4. a 4-input OR gate

3. Which of the following boolean expressions is ‘NOT TRUE’?

1. A + 1 = A
2. $A + \overline{A}=1$
3. A.A = A
4. $A.\overline{A}=0$

4. The complement form of $A(B+C)(\overline{C}+\overline{D})$ is

1. $A + \overline{B}\,\overline{C}+\overline{D}C=1$
2. A +BC + CD
3. A + BC
4. $\overline{A} + \overline{B}\,\overline{C}+CD$

5. The simplified form of the boolean expression $\overline{A} + A\overline{B}$ is

1. A + B
2. $A +\overline{B}$
3. $\overline{B} + A$
4. $\overline{A} + \overline{B}$

6. If A and B are boolean variables, then what is $(A + B).( A + \overline{B})$ is

1. B
2. A
3. A + B
4. AB

7. What is the boolean expression A ⊕ B equivalent to?

1. $AB+ \overline{A}\,\overline{B}$
2. $\overline{A}B + A\overline{B}$
3. B
4. $\overline{A}$

8. If x and y are boolean variables, which one of the following is the equivalent of  x ⊕ y ⊕ xy equivalent to?

1. $x+\overline{y}$
2. x + y
3. 0
4. 1

9. Which of the following boolean algebra rules is correct?

1. $A.\overline{A}=1$
2. A + AB = A + B
3. $A + \overline{A}B = A + B$
4. A(A+B) = B

10. The simplified logic form of a logic function

$Y=\overline{(\overline{A\overline{B}})(\overline{\overline{A}B})}$

1. A + B
2. AB
3. $\overline{A}+\overline{B}$
4. $\overline{A}B + A\overline{B}$

11. The boolean expression $Y=AB+ (A+B)(\overline{A}+B)$ may be simplified as

1. Y = A
2. $Y = \overline{A}$
3. Y = B
4. $Y = \overline{B}$

12. The reduced form of the boolean expression

$A[B+C(\overline{AB + AC})]$ is

1. $\overline{A}B$
2. $A\overline{B}$
3. AB
4. $AB+B\overline{C}$

13. Which one of the following statements is not correct?

1. $X+\overline{X}Y = X$
2. $X(\overline{X}+Y) = XY$
3. $XY + \overline{X}\,\overline{Y} = X$
4. $ZX + Z\overline{X}Y = ZX + ZY$

14. In boolean algebra, if $F = (A+B)(\overline{A}+C)$ then

1. $F = AB + \overline{A}C$
2. $F = AB + \overline{A}\,\overline{B}$
3. $F = AC + \overline{A}B$
4. $F = A\overline{A}+\overline{A}B$

15. The expression $(X+Y)(X+\overline{Y})(\overline{X}+Y)$ is equivalent to

1. $\overline{X}\,\overline{Y}$
2. $\overline{X}Y$
3. $X\overline{Y}$
4. XY