Given the Boolean expression , which of the following rows in the truth table would have an output of 1 (True)?

A = 1, B = 0, C = 1 Explanation: Logic Check XOR Part: Implication Part: Final Result: Final Equation

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NIMCET 2025 Computer PYQ — Given the Boolean expression , which of the following rows in the… | Mathem Solvex | Mathem Solvex

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NIMCET 2025 — Computer PYQ

NIMCET | Computer | 2025

Given the Boolean expression $(A \oplus B) \wedge (B \rightarrow C)$ , which of the following rows in the truth table would have an output of 1 (True)?

Choose the correct answer:

A.
A = 1, B = 1, C = 1
B.
A = 0, B = 1, C = 0
C.
A = 0, B = 0, C = 0
D.
A = 1, B = 0, C = 1
(Correct Answer)

Correct Answer:

A = 1, B = 0, C = 1

Explanation

Logic Check

XOR Part:

$(A \oplus B) \implies (1 \oplus 0) = 1$
Implication Part:

$(B \rightarrow C) \implies (0 \rightarrow 1) = 1$
Final Result:

$(1 \wedge 1) = 1$

Final Equation

(A \oplus B) \wedge (\bar{B} \vee C) = 1

Explanation

Logic Check

XOR Part:

$(A \oplus B) \implies (1 \oplus 0) = 1$
Implication Part:

$(B \rightarrow C) \implies (0 \rightarrow 1) = 1$
Final Result:

$(1 \wedge 1) = 1$

Final Equation

(A \oplus B) \wedge (\bar{B} \vee C) = 1

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