 # Important Questions Boolean Logic Class 11 Computer Science

Please refer to Important Questions Boolean Logic Class 11 Computer Science below. These questions and answers have been prepared based on the latest examination guidelines and NCERT book issued for Class 11 Computer Science for the current academic year. We have provided Important Questions for Class 11 Computer Science for all chapters here. Boolean Logic is an important chapter in Class 11 Computer Science, following Important Questions and their solutions will help you to get more marks in examinations.

## Boolean Logic Class 11 Computer Science Important Questions

Question: Prove X. (X+Y) = X using truth table.

Question: What is tautology?
Answer: If the result of any logical statement or expression is always TRUE or 1 for all input
combinations, it is called tautology.

Question: Give duals for the following –
(a) X+X‟Y (b) XY+XY‟+X‟Y (c) AB+A‟B (d) ABC+AB‟C+A‟BC‟
(b) (X+Y).(X+Y‘).(X‘+Y)
(c) (A+B).(A‘+B)
(d) (A+B+C).(A+B‘+C).(A‘+B+C‘)

Question: What is a truth table? What is its significance?
Answer: A truth table is a table which represents all the possible values of logical variables/statements
along with all the possible results of the given combinations of values.

Question: What is Fallacy?
Answer: If the result of any logical statement or expression is always FALSE or 0 for all input combinations, it is called fallacy.

Question: Prove X.(X+Y)=X by algebraic method.
Answer: L.H.S. X. (X+Y) = X.X + X.Y
= X+X.Y since X.X = X
= X.(1+Y)
= X (R.H.S.) since 1+Y = 1

Question: Find the complement of the following Boolean function : F1=AB‟ + C‟D‟
Answer: Complement of F1 will be (A‘+B).(C+D)

Question: Obtain the Boolean Expression for the logic circuit shown bellow –

Question: Prove algebraically X.Y + X‟.Z + Y.Z = X.Y + X‟.Z
Answer: L.H.S. X.Y + X‘.Z + Y.Z = X.Y + X‘.Z + 1.Y.Z
= X.Y + X‘Z + (X+X‘).Y.Z
= X.Y + X‘Z + X.Y.Z + X‘.Y.Z
= X.Y + X.Y.Z + X‘Z + X‘.Y.Z
= X.Y.(1+Z) + X‘.Z.(1+Y)
=X.Y + X‘.Z Since 1+Z= 1 and 1+Y = 1

Question: State and verify Involution law.
Answer: Involution law says that (X‘)‘ = X.

Question: Prove the complementarity law of Boolean algebra using truth table?

Question: State DeMorgan‟s law of Boolean Algebra and verify them using truth table.
Answer: (a) (X + Y)‘ = X‘.Y‘ (b) (X.Y)‘ = X‘ + Y‘

Question: What do you understand by “logical function”? Give examples for logical functions.
Answer: Boolean algebra is the algebra of logic that deals with the study of binary variables and logical operations. It was founded by the mathematician George Boole.Boolean variables are the variables which have only two states i.e. true/ false or right/ wrong or on/off or 0/1. Boolean function or more commonly known as a logic function is an expression expressed algebraically.There are 3 logical operators: AND, OR and NOT.

Question: Draw logic circuit diagram for the following expression –
(a) Y=AB+B‟C+C‟A‟ (b) R=XYZ‟ + Y.(X+Z‟)

Question: What are basic postulates of Boolean Algebra?10

Q.11 What does duality principal state? What is its usage in Boolean algebra?
Answer: The duality principle ensures that “if we exchange every symbol by its dual in a formula, we get
the dual result”.

• Everywhere we see 1, change to 0.
• Everywhere we see 0, change to 1.
• Similarly, (+) to (.) , and (.)to (+).
• For example if A+B=1 then its dual will be A.B=0

Question: Why are NAND and NOR Gates more popular?
Answer: The NOR Gate has two or more input signals but only one output signal. If all the inputs are 0
(i.e. low) then output signal is 1(high).

The NAND Gate has two or more input signals but only one output signal. If all the inputs are
(i.e. High) then output signal is 0(low).

NAND and NOR Gates are known as universal gates because fundamental gates can be made using them. And By using NAND and NOR Gates the cost and size of circuit gets reduced.

Question: Draw the AND OR Circuit for : y=AB‟C‟D‟ + ABC‟D‟ + ABCD 15

Question: Prove algebraically that (X+Y).(X+Z)=X+Y.Z
Answer: L.H.S. (X+Y).(X+Z) = X.X + X.Z + X.Y + Y.Z
=X + X.Z + X.Y + Y.Z Since X.X=X
=X + X.Y + Y.Z Since X+XZ=X
= X + Y.Z R.H.S. Since X+X.Y=X

Question: Make AND Gate using NAND Gate.

Question: Make OR Gate using NAND Gate.

Question:Make OR Gate using NOR Gate.

Question: Make NOT Gate using NAND Gate.