Question

Match the LIST-I with LIST-II

LIST-I (Logic Gates)		LIST-II (Expressions)
A.	EX-OR	I.	\( A\bar{B} + \bar{A}B \)
B.	NAND	II.	\( A + B \)
C.	OR	III.	\( AB \)
D.	EX-NOR	IV.	\( \bar{A}\bar{B} + AB \)

Choose the correct answer from the options given below:

• A. A - I, B - II, C - III, D - IV
• B. A - I, B - III, C - II, D - IV
• C. A - I, B - II, C - IV, D - III
• D. A - III, B - IV, C - I, D - II

Hint:

When facing matching questions with a potential error, first identify all the pairs you are certain about. Then, use the process of elimination to find the option that correctly matches all the unambiguous pairs. The remaining pair in that option is likely the intended, albeit flawed, answer.

Answer 1

The Correct Option is B

Step 1: Match each logic gate with its Boolean expression. - A. EX-OR: Outputs true when inputs differ. Expression: \( A \oplus B = A\bar{B} + \bar{A}B \). Matches expression I. Thus, A \(\rightarrow\) I. - C. OR: Outputs true if at least one input is true. Expression: \( A + B \). Matches expression II. Thus, C \(\rightarrow\) II. - D. EX-NOR: Outputs true when inputs are the same. Expression: \( \overline{A \oplus B} = AB + \bar{A}\bar{B} \). Matches expression IV. Thus, D \(\rightarrow\) IV. - B. NAND: The negation of the AND gate. Expression: \( \overline{AB} \). Expression III is \(AB\), the expression for an AND gate.
Step 2: Evaluate the options using the established matches. Confirmed matches: A\(\rightarrow\)I, C\(\rightarrow\)II, D\(\rightarrow\)IV. Reviewing options: - Option (1) states C\(\rightarrow\)III, which is incorrect. - Option (2) states A\(\rightarrow\)I, C\(\rightarrow\)II, and D\(\rightarrow\)IV. This option aligns with our findings but pairs B (NAND) with III (AND). This suggests a potential error in the question, where gate B should have been AND or expression III should have been \(\overline{AB}\). However, given the strong agreement of the other three pairings, this option is the most likely intended answer. - Option (3) states C\(\rightarrow\)IV, which is incorrect. - Option (4) states A\(\rightarrow\)III, which is incorrect. Based on the analysis, option (2) is the most plausible choice, assuming a typographical error in the question's pairings.