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Write the Boolean expression for
i. ?1? ii. ?2? iii. ?3? iv. ?4?
8. Given the following logic circuit. Write the Boolean expression for
i. ?1? ii. ?2? iii. ?3?
?1?
A ?3?
B ?2?
C
9. Draw the logic circuit diagram of the following boolean expression.
i. (A+B)'.(B+C)'.(C+A)'
ii. (A'.B + B'.C + C'.A)
iii. (A+B+C)'.B'C'
iv. (A'.B' + A.B)+(A.B)'
v. A'.B+A.(B+B'.C)
D. Assertion and Reasoning Based Question.
Assertion: A compound proposition is truth-functional.
Reason: A compound proposition accepts truth values as input and produces a unique truth value as output.
(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.
#Problem Solving & Logical Reasoning
#Coding & Computational Thinking
Previous Years' Questions
1. If A = “It is cloudy” and B = “It is raining”, then write the proposition for:
(i) Contrapositive (ii) Converse [ISC 2019]
Ans. (i) If it is not raining, then it is not cloudy. (ii) If it is raining, then it is cloudy.
2. Using a truth table, state whether the following proposition is a Tautology, Contradiction or Contingency:
∼(P → Q) ↔ (∼P ∨ Q) [ISC 2019]
Ans. P Q P → Q ∼(P → Q) ∼P ∨ Q ∼(P → Q) ↔ (∼P ∨ Q)
0 0 1 0 1 0
0 1 1 0 1 0
1 0 0 1 0 0
1 1 1 0 1 0
Hence, it is a contradiction.
3. What is a half adder? Write the truth table and derive an SOP expression for sum and carry for a half adder. [ISC 2019]
Ans. The half adder is a combinational circuit that is designed to perform the addition of two bits and produce the two binary
outputs as sum (S) and carry (C) bits.
Truth table for half adder is:
Input Output
A B Sum Carry
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
SOP expression for sum term = A'.B + A.B'
SOP expression for carry term = A.B
9494 Touchpad Computer Science-XI

