Question

Which logic gate is represented by the following combinations of logic gates?

• A. NAND
• B. AND
• C. NOR
• D. OR

Hint:

Logic simplification: Use De Morgan’s theorem. Track inversions carefully.

Answer 1

The Correct Option is A

Concept: Use De Morgan's laws. Step 1: {\color{red}Identify components.} - Inputs A and B first pass through NOT gates ⇒ \( \bar{A}, \bar{B} \). - These go into OR gate with inversion at output ⇒ NOR of inverted inputs. Step 2: {\color{red}Expression.} \[ Y = \overline{\bar{A} + \bar{B}} \] Step 3: {\color{red}Apply De Morgan.} \[ Y = A \cdot B \] But inversion at output gives complement: \[ Y = \overline{AB} \] Step 4: {\color{red}Conclusion.} This is NAND gate.