question_answer

A system of logic gates is shown in the figure. From the study of truth table it can be found that to produce a high output (1) at R, we must have

A) \[X=0,\,Y=1\]

B)  \[X=1,\,Y=1\]

C)  \[X=1,\,Y=0\]

D)  \[X=0,\,Y=0\]

Correct Answer: C

Solution :

 The truth table can be written as

\[X\]	\[Y\]	\[\bar{X}\]	\[\bar{Y}\]	\[P=\bar{X}+Y\]	\[Q=\overline{X.Y}\]	\[R=\overline{P+Q}\]
0	1	1	0	1	1	0
1	1	0	0	1	1	0
1	0	0	1	0	0	1
0	0	1	1	1	1	0

So, \[X=1,Y=0\]gives output \[R=1.\]