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: Analyze each logic gate and its corresponding Boolean expression. - A. EX-OR: The Exclusive-OR gate outputs true only when the inputs are different. Its expression is \( A \oplus B = A\bar{B} + \bar{A}B \). This matches expression I. So, A \(\rightarrow\) I. - C. OR: The OR gate outputs true if at least one input is true. Its expression is \( A + B \). This matches expression II. So, C \(\rightarrow\) II. - D. EX-NOR: The Exclusive-NOR gate outputs true only when the inputs are the same. Its expression is \( \overline{A \oplus B} = AB + \bar{A}\bar{B} \). This matches expression IV. So, D \(\rightarrow\) IV. - B. NAND: The NAND gate is the negation of the AND gate. Its expression is \( \overline{AB} \). Expression III is \(AB\), which is the expression for an AND gate.
Step 2: Evaluate the options based on the correct matches. We have confirmed: A\(\rightarrow\)I, C\(\rightarrow\)II, D\(\rightarrow\)IV. Let's check the given options: - Option (1) has C\(\rightarrow\)III, which is incorrect. - Option (2) has A\(\rightarrow\)I, C\(\rightarrow\)II, and D\(\rightarrow\)IV. This aligns with our findings. It matches B (NAND) with III (AND). This implies a likely error in the question, where gate B should have been AND, or expression III should have been \(\overline{AB}\). However, given the other three perfect matches, this option is the most plausible intended answer. - Option (3) has C\(\rightarrow\)IV, which is incorrect. - Option (4) has A\(\rightarrow\)III, which is incorrect. Therefore, option (2) is the correct choice, assuming a typo in the question's list.