Answer the following.
Verify if $(A + A')'$ is a Tautology, Contradiction, or a Contingency.
Show answer
Answer
AI| A | A' | A + A' | (A + A')' |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
Boolean Algebra - ISC Class 12 Computer Science Questions with Answers, Page 6
189 past-paper questions on Boolean Algebra from ISC Class 12 Computer Science papers (2026-2017), newest first, in full. Questions 101-120 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.
Nothing matches. Try fewer letters.
Answer the following.
Write the minterm of $F(A, B, C, D)$ when $A = 1, B = 0, C = 0$ and $D = 1$.
Show answer
Answer
AIIn a minterm a variable with value 1 is written as it is and a variable with value 0 is complemented.
Minterm $= A \cdot B' \cdot C' \cdot D$ (i.e. $AB'C'D$, $m_9$).
Answer the following.
The reduced expression of the Boolean function $F(P, Q) = P' + PQ$ is:
- (a)$P' + Q$
- (b)$P$
- (c)$P'$
- (d)$P + Q$
Show answer
Answer
AICorrect option: (a)
Answer: (a) $P' + Q$
$P' + PQ = (P' + P)(P' + Q) = 1 \cdot (P' + Q) = P' + Q$ (distributive law, then complement law).
Answer the following.
Convert the following cardinal expression to its canonical form:
$F(P, Q, R) = \pi(0, 1, 3, 4)$
Show answer
Answer
AI$F(P, Q, R) = \pi(0, 1, 3, 4)$: write each maxterm in binary; a 0 bit gives the variable as it is and a 1 bit gives its complement, and the variables within a term are added.
$0 = 000 \to (P + Q + R)$
$1 = 001 \to (P + Q + R')$
$3 = 011 \to (P + Q' + R')$
$4 = 100 \to (P' + Q + R)$
Canonical form: $F(P, Q, R) = (P + Q + R) \cdot (P + Q + R') \cdot (P + Q' + R') \cdot (P' + Q + R)$
Reduce the following using a Karnaugh map.
Given the Boolean function $F(A, B, C, D) = \Sigma(0, 1, 2, 3, 4, 6, 9, 11, 13)$.
(a)[4.0]
Reduce the above expression 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
Must show: variables and their complements as inputs
Show answer
Answer (b)
AILogic gate diagram for $F = A'D' + B'D + AC'D$: two 2-input AND gates and one 3-input AND gate feeding a 3-input OR gate.
Choose the correct option.
The dual of $(P + P') \cdot (Q + 0) = Q$ is:
- (a)$P \cdot P' + Q \cdot 1 = Q$
- (b)$P \cdot P' + Q \cdot 0 = Q$
- (c)$P \cdot P + Q \cdot 1 = Q'$
- (d)$P + P' + Q + 1 = Q$
Show answer
Answer
AICorrect option: (a)
Answer: (a) $P \cdot P' + Q \cdot 1 = Q$
The dual of an expression is formed by interchanging every $+$ with $\cdot$ and every $0$ with $1$ (variables are left unchanged): $(P+P')\cdot(Q+0)=Q$ becomes $(P\cdot P')+(Q\cdot 1)=Q$.
Answer the following.
Verify the following expression by using the truth table:
$(A \odot B)' = (A \oplus B)$
No answer yet.
Answer the following using a truth table.
A family intends to purchase a smart phone depending on the criteria given below:
• Quad core processor with internal memory of 64 GB or more but not a resale phone
OR
• Resale phone with quad core processor but without warranty
OR
• Processor is not a quad core but with a warranty of 1 year and the internal memory is of 64 GB or more
The inputs are:
(In all the above cases, 1 indicates yes and 0 indicates no.)
Output: X [1 indicates purchased, 0 indicates not purchased for all cases]
Draw the truth table for the inputs and outputs given above and write the SOP expression
| INPUTS | |
|---|---|
| P | Quad core processor |
| M | Internal memory of 64 GB or more |
| R | Resale phone |
| W | Warranty of 1 year |
No answer yet.
Choose the correct option.
If $(x \Rightarrow \sim y)$ then, its inverse will be:
- (a)$x \Rightarrow y$
- (b)$y \Rightarrow x$
- (c)$\sim y \Rightarrow x$
- (d)$\sim x \Rightarrow y$
Show answer
Answer
AICorrect option: (d)
Answer: (d) $\sim x => y$
For an implication $p \Rightarrow q$, its inverse is $\sim p \Rightarrow \sim q$. Here $p=x$ and $q=\sim y$, so the inverse is $\sim x \Rightarrow \sim(\sim y) = \sim x \Rightarrow y$.
Choose the correct option.
The Quad group in a Karnaugh’s map eliminates:
- (a)One variable
- (b)Four variables
- (c)Three Variables
- (d)Two variables
Show answer
Answer
AICorrect option: (d)
Answer: (d) Two variables
A quad (group of 4 cells) eliminates two variables; a pair eliminates one and an octet three.
Choose the correct option.
The propositional operator $=>$ represents:
- (a)Conjunction
- (b)Implication
- (c)Disjunction
- (d)Negation
Show answer
Answer
AICorrect option: (b)
Answer: (b) Implication
The operator => stands for implication (if ... then).
Choose the correct option.
the converse of the proposition is:
- (i)~Q => P
- (ii)Q => ~P
- (iii)~Q => ~P
- (iv)~P => ~Q
Show the case
With reference to the given proposition $\sim P => Q$, answer the following questions:
Show answer
Answer
AICorrect option: (ii)
Answer: (ii) Q => ~P
The converse of A => B is B => A. Here A = ~P, B = Q, so the converse is Q => ~P.
Choose the correct option.
The reduced expression of the Boolean function given above is:
- (i)$(B + C) \cdot (B + D) \cdot (A' + D)$
- (ii)$BC + BD + A'D$
- (iii)$AB' + C'D' + B'D'$
- (iv)$(A + B') \cdot (C' + D') \cdot (B' + D')$
Show the case
Reduce the given Boolean function $F(A,B,C,D) = \pi(3,4,5,6,7,11,13,15)$ by using 4-variable Karnaugh map and answer the following questions:
Show answer
Answer
AICorrect option: (iv)
Answer: (iv) $(A + B') \cdot (C' + D') \cdot (B' + D')$
The three quads give $(A+B')$ (4,5,6,7), $(B'+D')$ (5,7,13,15) and $(C'+D')$ (3,7,11,15).
Choose the correct option.
The complement of the expression:
- (i)$P'R' + (P' + Q') \cdot (Q' + R)$
- (ii)$(P' + R') \cdot (P' + Q') + (Q + R')$
- (iii)$P'R' \cdot (PQ' + Q'R)$
- (iv)$(P + R)' \cdot (P' + Q) \cdot (Q' + R)$
Show the case
Given the Boolean expression $F = (P + R) \cdot (P \cdot Q + Q \cdot R')$, identify:
Show answer
Answer
AICorrect option: (i)
Answer: (i) $P'R' + (P' + Q') \cdot (Q' + R)$
By De Morgan's law, $F' = (P+R)' + (PQ + QR')' = P'R' + (P'+Q')(Q'+R)$.
Choose the correct option.
the contra-positive of the proposition is:
- (i)~P => Q
- (ii)Q => P
- (iii)~Q => P
- (iv)~P => ~Q
Show answer
Answer
AICorrect option: (iii)
Answer: (iii) ~Q => P
The contrapositive of A => B is ~B => ~A. Here it is ~Q => ~(~P) = ~Q => P.
Choose the correct option.
The POS expression for $X(A,B,C,D)$ will be:
- (i)$F(A,B,C,D) = \sum(3, 5, 7, 11, 12, 13, 14, 15)$
- (ii)$F(A,B,C,D) = \pi(3, 5, 7, 11, 12, 13, 14, 15)$
- (iii)$F(A,B,C,D) = \pi(0, 1, 2, 4, 6, 8, 9, 10)$
- (iv)$F(A,B,C,D) = \sum(0, 1, 2, 4, 6, 8, 9, 10)$
Show the case
A school intends to select candidates for an Inter school competition as per the criteria given below:
• The student has participated in an earlier competition and is very creative
Or
• The student is very creative and has excellent general awareness, but has not participated in any competition earlier
Or
• The student has excellent general awareness and has won prize in an inter-house competition
The inputs are:
(In all the above cases 1 indicates yes and 0 indicates no).
Output: X [1 indicates yes and 0 indicates no for all cases].
| Inputs | |
|---|---|
| A | Participated in a competition earlier |
| B | Is very creative |
| C | Won prize in an inter house competition |
| D | Has excellent general awareness |
Show answer
Answer
AICorrect option: (iii)
Answer: (iii) $F(A,B,C,D) = \pi(0, 1, 2, 4, 6, 8, 9, 10)$
X = AB + A'BD + CD, which is 1 for minterms 3,5,7,11,12,13,14,15. The POS form lists the remaining maxterms 0,1,2,4,6,8,9,10.
Choose the correct option.
The proposition $(a <=> b)$ is represented by:
- (a)$a'b' + ab$
- (b)$(a' + b') \cdot (a + b)$
- (c)$(a + b)'$
- (d)$(a \cdot b)'$
Show answer
Answer
AICorrect option: (a)
Answer: (a) $a'b' + ab$
The biconditional a <=> b is true when both are equal: $ab + a'b'$ (XNOR).
Choose the correct option.
The law which represents the Boolean equation $A + B = B + A$ is:
- (a)Associative Law
- (b)Distributive Law
- (c)Commutative Law
- (d)Absorption Law
Show answer
Answer
AICorrect option: (c)
Answer: (c) Commutative Law
A + B = B + A shows the order of operands does not matter, which is the Commutative Law.
Choose the correct option.
The complement of the Boolean expression $F(P,Q,R) = (P + Q + R)$ is:
- (a)$P'Q'R'$
- (b)$P' + Q' + R'$
- (c)$P + (Q' + R')$
- (d)$(P + Q) + R'$
Show answer
Answer
AICorrect option: (a)
Answer: (a) $P'Q'R'$
By De Morgan's law, $(P+Q+R)' = P'Q'R'$.
Choose the correct option.
If $A = 1, B = 0, C = 0$ and $D = 1$, then the maxterm will be:
- (a)$AB'C'D$
- (b)$A'BCD'$
- (c)$A + B' + C' + D$
- (d)$A' + B + C + D'$
Show answer
Answer
AICorrect option: (d)
Answer: (d) $A' + B + C + D'$
A maxterm is a sum in which a variable appears complemented if its value is 1 and uncomplemented if 0. For A=1, B=0, C=0, D=1 this gives $A' + B + C + D'$.