1. In boolean algebra, the OR operation is performed by which properties?
a) Associative properties
b) Commutative properties
c) Distributive properties
d) All of the Mentioned
Explanation: The expression for Associative property is given by A+(B+C) = (A+B)+C & A*(B*C) = (A*B)*C.
The expression for Commutative property is given by A+B = B+A & A*B = B*A.
The expression for Distributive property is given by A+BC=(A+B)(A+C) & A(B+C) = AB+AC.
2. The expression for Absorption law is given by _________
a) A + AB = A
b) A + AB = B
c) AB + AA’ = A
d) A + B = B + A
Explanation: The expression for Absorption Law is given by: A+AB = A.
Proof: A + AB = A(1+B) = A (Since 1 + B = 1 as per 1’s Property).
3. According to boolean law: A + 1 = ?
a) 1
b) A
c) 0
d) A’
Explanation: A + 1 = 1, as per 1’s Property.
4. The involution of A is equal to _________
a) A
b) A’
c) 1
d) 0
Explanation: The involution of A means double inversion of A (i.e. A”) and is equal to A.
Proof: ((A)’)’ = A
5. A(A + B) = ?
a) AB
b) 1
c) (1 + AB)
d) A
Explanation: A(A + B) = AA + AB (By Distributive Property) = A + AB (A.A = A By Commutative Property) = A(1 + B) = A*1 (1 + B = 1 by 1’s Property) = A.
6. DeMorgan’s theorem states that _________
a) (AB)’ = A’ + B’
b) (A + B)’ = A’ * B
c) A’ + B’ = A’B’
d) (AB)’ = A’ + B
Explanation: The DeMorgan’s law states that (AB)’ = A’ + B’ & (A + B)’ = A’ * B’, as per the Dual Property.
7. (A + B)(A’ * B’) = ?
a) 1
b) 0
c) AB
d) AB’
Explanation: The DeMorgan’s law states that (AB)’ = A’ + B’ & (A + B)’ = A’ * B’, as per the Dual Property.
8. Complement of the expression A’B + CD’ is _________
a) (A’ + B)(C’ + D)
b) (A + B’)(C’ + D)
c) (A’ + B)(C’ + D)
d) (A + B’)(C + D’)
Explanation: (A’B + CD’)’ = (A’B)'(CD’)’ (By DeMorgan’s Theorem) = (A” + B’)(C’ + D”) (By DeMorgan’s Theorem) = (A + B’)(C’ + D).
9. Simplify Y = AB’ + (A’ + B)C.
a) AB’ + C
b) AB + AC
c) A’B + AC’
d) AB + A
Explanation: Y = AB’ + (A’ + B)C = AB’ + (AB’)’C = (AB’ + C)( AB’ + AB’) = (AB’ + C).1 = (AB’ + C).
10. The boolean function A + BC is a reduced form of ____________
a) AB + BC
b) (A + B)(A + C)
c) A’B + AB’C
d) (A + C)B
Explanation: (A + B)(A + C) = AA + AC + AB + BC = A + AC + AB + BC (By Commutative Property) = A(1 + C + B) + BC = A + BC (1 + B + C =1 By 1’s Property).