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Boolean Algebra - ISC Class 12 Computer Science Questions with Answers, Page 4

189 past-paper questions on Boolean Algebra from ISC Class 12 Computer Science papers (2026-2017), newest first, in full. Questions 61-80 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.

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2025 · 1 mark · MCQOpen: The Associative Law states that:

Choose the correct option.

The Associative Law states that:
  • (a)$A \cdot B = B \cdot A$
  • (b)$A + B = B + A$
  • (c)$A \cdot (B + C) = A \cdot B + A \cdot C$
  • (d)$A + (B + C) = (A + B) + C$
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Answer

AI

Correct option: (d)

Answer: (d) $A + (B + C) = (A + B) + C$ The Associative Law states that the grouping of operands does not affect the result when the same operator is applied repeatedly.
2025 · 1 mark · Assertion-reasonOpen: In Boolean Algebra, dual of the Boolean expression is equal to .

Study the Assertion and Reason and choose the correct option.

Assertion: In Boolean Algebra, dual of the Boolean expression $(A+B)'.1$ is equal to $0$.

Reason: In Boolean Algebra, the complement of an OR operation is equal to the AND operation of complement of the individual variables.

  • (a)Both A and R are true, and R is the correct explanation of A.
  • (b)Both A and R are true, but R is not the correct explanation of A.
  • (c)A is true, but R is false.
  • (d)A is false, but R is true.
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Answer

AI

Correct option: d

Answer: (d) A is false, but R is true. The dual of (A+B)'.1 is formed by swapping + with . and 1 with 0: (A.B)' + 0, which simplifies to A'+B' (equivalently (A.B)') - a contingency, not the constant 0, so A is false. R correctly states De Morgan's law, (A+B)' = A'.B', so R is true.
2024 · 1 mark · MCQOpen: Idempotence Law states that:

Choose the correct option.

Idempotence Law states that:
  • (a)$X + X = X$
  • (b)$X + X' = 0$
  • (c)$X + X = 1$
  • (d)$X + X' = X$
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Answer

AI

Correct option: (a)

Answer: (a) $X + X = X$ The Idempotence Law states that ORing (or ANDing) a variable with itself gives back the same variable.
2024 · 5 marks · Truth tableOpen: To be recruited as the Principal in a renowned College, a candidate must…

Answer the following using a truth table.

To be recruited as the Principal in a renowned College, a candidate must satisfy any one of the following criteria: • The candidate must be a Postgraduate and should either possess a B.Ed. degree or a teaching experience of more than 15 years. OR • The candidate must be an employee of the same college with a teaching experience of more than 15 years. OR • The candidate must be a Postgraduate but not an employee of the same college and should have a teaching experience of more than 15 years. The inputs are:
INPUTS
PCandidate is a Postgraduate
SCandidate is an employee of the same College
ECandidate has a teaching experience of more than 15 years
BCandidate possesses a B.Ed. degree
(In all the above cases, 1 indicates yes and 0 indicates no) Output: X - Denotes eligibility of a candidate [1 indicates eligibility and 0 indicates ineligibility in all cases] Draw the truth table for the inputs and outputs given above and write the SOP expression for X (P, S, E, B).

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2024 · 1 mark · NumericalOpen: If and then find the value of

Answer the following.

If $A=1$ and $B=0$ then find the value of $(A' + 1) \cdot B$
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Answer

AI
$(A'+1) \cdot B$ for $A=1, B=0$: $A'=0$, so $A'+1 = 0+1 = 1$ (Identity Law: anything OR 1 = 1). Then $1 \cdot B = 1 \cdot 0 = 0$.

Final answer: 0

2024 · 1 mark · MCQOpen: The complement of the Boolean expression is:

Choose the correct option.

The complement of the Boolean expression $(X \cdot Y)' + Z'$ is:
  • (a)$(X + Y) \cdot Z$
  • (b)$X \cdot Y \cdot Z$
  • (c)$(X' + Y') \cdot Z'$
  • (d)$(X' + Y') \cdot Z$
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Answer

AI

Correct option: (b)

Answer: (b) $X \cdot Y \cdot Z$ By De Morgan's Law: $[(X \cdot Y)' + Z']' = [(X \cdot Y)']' \cdot [Z']' = (X \cdot Y) \cdot Z = X \cdot Y \cdot Z$.
2024 · 5 marks · K-mapOpen: Reduce the Boolean function by using 4-variable Karnaugh map, showing the…

Reduce the following using a Karnaugh map.

Reduce the Boolean function $F(A, B, C, D) = \pi(0, 2, 4, 6, 8, 9, 10, 11, 14)$ by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs). Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

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2024 · 1 mark · MCQOpen: The equivalent of will be:

Choose the correct option.

The equivalent of $P \land Q \lor \sim P \land \sim Q$ will be:
  • (a)$((P \land Q) \lor \sim P) \land \sim Q$
  • (b)$(P \land Q) \lor (\sim P \land \sim Q)$
  • (c)$P \land (Q \lor \sim P) \land \sim Q$
  • (d)$P \land (Q \lor (\sim P \land \sim Q))$
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Answer

AI

Correct option: (b)

Answer: (b) $(P \land Q) \lor (\sim P \land \sim Q)$ Since $\land$ (AND) has higher precedence than $\lor$ (OR), $P \land Q \lor \sim P \land \sim Q$ is evaluated as $(P \land Q) \lor (\sim P \land \sim Q)$.
2024 · 1 mark · Assertion-reasonOpen: and and minterm is Which one of the following options is correct?

Study the Assertion and Reason and choose the correct option.

Assertion: $A=0\quad B=1\quad C=0$ and $D=1$ and minterm is $A' \cdot B \cdot C' \cdot D$

Reason: The final sum term must be $0$ so $A$ and $C$ are complemented.

Which one of the following options is correct?
  • (a)Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.
  • (b)Both Assertion and Reason are true, but Reason is not the correct explanation for Assertion.
  • (c)Assertion is true and Reason is false.
  • (d)Assertion is false and Reason is true.
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Answer

AI

Correct option: (c)

The Assertion is true: for a minterm, a variable is written uncomplemented if its value is 1 and complemented if its value is 0; here $A=0, B=1, C=0, D=1$ gives exactly $A'BC'D$, which matches the given minterm. The Reason is false: it calls this a 'sum term' that 'must be 0', but that is the rule for forming a MAXTERM (POS) - a minterm is a PRODUCT term that must evaluate to 1, not a sum term equal to 0; so the Reason's stated justification is incorrect even though its numeric conclusion happens to agree. Answer: (c) Assertion is true and Reason is false.
2024 · 1 mark · Assertion-reasonOpen: For proposition , its contrapositive is

Study the Assertion and Reason and choose the correct option.

Assertion: For proposition $\sim A \Rightarrow B$, its contrapositive is $B \Rightarrow \sim A$

Reason: Contrapositive is the converse of inverse for any proposition.

  • (a)Both Assertion and Reason are true, and Reason is the correct explanation for the Assertion.
  • (b)Both Assertion and Reason are true, but Reason is not the correct explanation for the Assertion.
  • (c)Assertion is true but Reason is false.
  • (d)Assertion is false but Reason is true.
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Answer

AI

Correct option: (d)

The Assertion is false: the contrapositive of $\sim A \Rightarrow B$ is $\sim B \Rightarrow A$, not $B \Rightarrow \sim A$. The Reason is true: the contrapositive of a proposition is indeed the converse of its inverse, in general. Since the Assertion is false, the Reason cannot be its explanation. Answer: (d)
2024 · 4 marks · DerivationOpen: From the logic circuit diagram given below, name the outputs (1), (2) and (3)…

Answer the following.

From the logic circuit diagram given below, name the outputs (1), (2) and (3) and finally derive the Boolean expression (F) and simplify it. Identify the propositional connective which is equivalent to the simplified Boolean expression.
Figure for this question
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Answer

AI
Outputs: (1) = X+Y', (2) = X.Z, (3) = (X+Y').(X.Z). Simplifying, F(X,Y,Z) = (3) + Z' = X + Z', which is logically equivalent to the propositional connective IMPLICATION, $Z \Rightarrow X$.
  1. (1) = X + Y' - output of the top OR gate, combining input X with Y' (from the NOT gate on Y).
  2. (2) = X . Z - output of the AND gate, combining input X (same branch that feeds gate (1)) with input Z.
  3. (3) = (1).(2) = (X+Y').(X.Z) - output of the middle AND gate, combining outputs (1) and (2).
  4. By the Distributive Law: (X+Y').(X.Z) = X.Z.X + X.Z.Y' = X.Z + X.Y'.Z (using the Idempotent Law X.X=X).
  5. X.Z + X.Y'.Z = X.Z.(1+Y') = X.Z (by the Distributive Law and the Identity Law 1+Y'=1); equivalently, by the Absorption Law X.(X+Y')=X, so (3) = X.Z directly.
  6. F = (3) + Z' - output of the final OR gate, combining (3) with Z' (from the bottom NOT gate on Z): F = X.Z + Z'.
  7. By the identity A + A'.B = A + B (with A=Z', B=X): Z' + Z.X = Z' + X.
  8. Therefore F(X,Y,Z) = X + Z'.
  9. X + Z' is equivalent to the propositional connective Implication, Z => X, since P=>Q is equivalent to (~P v Q); here Z=>X is equivalent to Z'+X = X+Z'.
2024 · 5 marks · K-mapOpen: Reduce the above expression X (P, S, E, B) by using 4-variable Karnaugh map…

Reduce the following using a Karnaugh map.

Reduce the above expression X (P, S, E, B) by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs). Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

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2024 · 1 mark · Short answerOpen: Define Canonical form of an expression with respect to its Cardinal form.

Answer the following.

Define Canonical form of an expression with respect to its Cardinal form.
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Answer

AI
The Canonical form of a Boolean expression is its complete standard form - canonical SOP (sum of minterms) or canonical POS (product of maxterms) - in which every term contains all the variables of the function, each appearing either in true or complemented form. The Cardinal form is simply the compact shorthand way of writing this canonical form: it lists only the decimal numbers of the minterms/maxterms using the symbol $\Sigma$ (for sum of minterms) or $\Pi$ (for product of maxterms), e.g. $F(A,B,C)=\Sigma m(1,3,7)$ is the Cardinal form of the canonical SOP $A'B'C + A'BC + ABC$.
2024 · 1 mark · One wordOpen: Write the cardinal form of the maxterm

Answer the following.

Write the cardinal form of the maxterm $X + Y' + Z$
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Answer

AI
The maxterm $X+Y'+Z$ corresponds to binary code $XYZ = 010$ (an uncomplemented variable is read as 0, a complemented variable as 1), i.e. decimal 2. Cardinal form: $M_2$.
2024 · 5 marks · Case basedOpen: Reduce the Boolean function by using 4-variable Karnaugh map, showing the…

Reduce the following using a Karnaugh map.

$F(A,B,C,D) = \pi (0, 1, 2, 3, 4, 6, 9, 11, 13)$
(a)[4.0]
Reduce the Boolean function $F(A,B,C,D) = \pi (0, 1, 2, 3, 4, 6, 9, 11, 13)$ by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).
(b)[1.0]
Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

Draw: logic gate diagram for the reduced expression

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Answer (b)

AI
Logic gate diagram for $F(A,B,C,D) = (A+D) \cdot (B+D') \cdot (A'+C+D')$: three OR gates feeding one AND gate.
Diagram for this answer
2024 · 1 mark · MCQOpen: According to the Principle of duality, the Boolean equation will be equivalent…

Choose the correct option.

According to the Principle of duality, the Boolean equation $(P + Q') \cdot R \cdot 1 = P \cdot R + Q' \cdot R$ will be equivalent to:
  • (a)$P \cdot Q' + R + 1 = (P + R) \cdot (Q' + R)$
  • (b)$P \cdot Q' + R + 0 = (P + R) \cdot (Q' + R)$
  • (c)$P' \cdot Q + R + 1 = (P' \cdot R') \cdot (Q + R')$
  • (d)$P \cdot Q' + R \cdot 0 = (P + R) \cdot (Q' + R)$
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Answer

AI

Correct option: (b)

Answer: (b) $P \cdot Q' + R + 0 = (P + R) \cdot (Q' + R)$ By the Principle of Duality, every $\cdot$ is replaced by $+$, every $+$ is replaced by $\cdot$, and every $1$ is replaced by $0$ (variables unchanged). Applying this to $(P+Q') \cdot R \cdot 1 = P \cdot R + Q' \cdot R$ gives $P \cdot Q' + R + 0 = (P + R) \cdot (Q' + R)$, which is option (b).
2024 · 1 mark · MCQOpen: Absorption law states that:

Choose the correct option.

Absorption law states that:
  • (a)$A \cdot ( A' + B) = A$
  • (b)$A + ( A \cdot B) = A$
  • (c)Both (a) and (b)
  • (d)$A \cdot ( B + C ) = A \cdot B + A \cdot C$
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Answer

AI

Correct option: (b)

Answer: (b) $A + (A \cdot B) = A$ This is the Absorption Law. Option (a) $A \cdot (A' + B)$ expands (by the Distributive Law) to $A \cdot A' + A \cdot B = 0 + AB = AB$, which is not equal to $A$ in general (e.g. $A=1, B=0$ gives $AB=0 \neq A=1$), so (a), and hence (c), are not valid absorption identities.
2024 · 1 mark · Assertion-reasonOpen: Boolean algebra and Binary number system are different from each other.

Study the Assertion and Reason and choose the correct option.

Assertion: Boolean algebra and Binary number system are different from each other.

Reason: There are some basic operations like AND, OR and NOT which are performed only in Boolean algebra.

  • (a)Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.
  • (b)Both Assertion and Reason are true, but Reason is not the correct explanation for Assertion.
  • (c)Assertion is true and Reason is false.
  • (d)Assertion is false and Reason is true.
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Answer

AI

Correct option: (a)

Both the Assertion and the Reason are true. Boolean algebra (a system of logic with values 0/1 and operators AND, OR, NOT used to evaluate logical statements) is indeed different from the Binary number system (a positional number system in base 2 used to represent numeric quantities, with arithmetic operators like addition), even though both use only the digits 0 and 1. The Reason correctly explains this: basic logical operations such as AND, OR and NOT are defined and performed only in Boolean algebra, not as standard operations of the binary number system. Answer: (a) Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.

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