Question 102

Computer Awareness Boolean algebra Medium

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

(A) A=1, B=1, C=1
(B) A=0, B=1, C=0
(C) A=1, B=0, C=1
(D) A=0, B=0, C=0
✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

\[ X = (A \oplus B) \land (B \to C) \] \[ \text{Recall: } A \oplus B = (A \land \overline{B}) \lor (\overline{A} \land B), \quad B \to C = \overline{B} \lor C \] \[ \begin{array}{|c|c|c||c|c||c|} \hline A & B & C & A \oplus B & B \to C & X = (A \oplus B)\land(B \to C) \\ \hline 1 & 1 & 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ \hline \end{array} \] \[ \text{Hence, the only row where } X = 1 \text{ is: } A=1, \, B=0, \, C=1 \] \[ \boxed{\text{Option C}} \]

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