Question

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. $X=0,Y=0$

Answer 1

The correct option is C $X=1,Y=0$

The truth table can be written as

$X$	$Y$	$\overline{X}$	$\overline{X}$	$P=\overline{X}+Y$	$Q=\overline{X+Y}$	$R=\overline{P+Q}$
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 $R=1$