GATE CSE 2025 | Set 2 | Question: 21

Question

​Consider the following logic circuit diagram.

Which is/are the CORRECT option(s) for the output function $F$ ?

• A. $\overline{X Y}$
• B. $\overline{X}+\overline{Y}+X \overline{Y}$
• C. $\overline{XY}+\overline{X}+X \overline{Y}$
• D. $X+\overline{Y}$

Comments

@Arjun sir, @Shaik Masthan sir , in go book the option C is wrongly printed.

Answer 1

The correct expreesion $F=\overline {XY}+\bar X+X\bar Y$ (Option C)

apply distributive law we get

$F=\overline {XY}+(\bar X+X).(\bar X+\bar Y)$

$F=\overline {XY}+(\bar X+\bar Y)$ (Option B)

apply demorgon's law here as $\overline {XY}=\bar X+\bar Y$,we get

$F=\overline {XY}+\overline {XY}=\overline {XY}$ (Option A)

Options $A,B,C$ are correct.

 

Comments

option galat print haa

 

---

its actually option A,C,D

---

haa 3rd option should be XY whole bar

Answer 2

According to given circuit (C) expression is correct

TRUTH TABLE

X	Y	OP.A	OP.B	OP.C	OP.D
0	0	1	1	1	1
0	1	1	1	1	0
1	0	1	1	1	1
1	1	0	0	0	1

 

SO, A,B,C OPTION SATISFY THIS QUESTION

ANS-A,B,C

Comments

it is the best method for these MSQ type questions

---

if there are more than 2 variables it woud be time consuming

 

Answer 3

Correct options are: A ,B , C

 

Answer 4

c

Answer 5

From the given circuit: a NAND gate takes inputs X, Y directly, giving (XY)'; a separate inverter taps the X line alone, giving X'; and a third branch inverts Y then ANDs it with X, giving XY'. All three signals feed into a final OR gate:

F = (XY)' + X' + XY'

By De Morgan's law, (XY)' = X' + Y', so this simplifies to F = X' + Y' + XY'. But the term XY' is already fully covered/absorbed by Y' alone (whenever XY' is true, Y' is automatically true too) — so by the absorption law, F = X' + Y' exactly, which is the same function as (XY)' itself.

So (XY)', X' + Y' + XY', and (XY)' + X' + XY' are all just different (redundant) ways of writing the exact same underlying function; only X + Y' is a genuinely different function.

Answer: (XY)'; X' + Y' + XY'; and (XY)' + X' + XY' (all equivalent, all correct).