UGC NET CSE | December 2005 | Part 2 | Question: 9

Question

Consider the following circuit :

to make it a Tautology the $?$ should be :

• A. $\text{NAND}$ gate
• B. $\text{AND}$ gate
• C. $\text{OR}$ gate
• D. $\text{EX-OR}$ gate

Answer 1

To get tautology output of $F$ should be $1$.

option 1) $F=(x+y)+ \overline{xy}$

applying de-morgon’s law:

$F=x+y+ \bar x+\bar y$

$F=(x+\bar x)+(y+\bar y)$

$F=1 (\because x+\bar x=1) $

So option $A$ ,$\text{NAND gate}$ is correct.

we can check remaining options but none of them give $1$ as output.