d
અહી \({\text{Y}}\,\, = \,\overline {Q.\,R}  \,\, = \,\,\overline Q  \, + \,\,\overline R \,\, = \,A.P + \,\,P.B\)

\(Y\,\, = \,\,P.\left( {A\,\, + \;\,B} \right)\,\, = \,\,\left( {\overline {A.B} } \right)\,\,.\,\,\left( {A\,\, + \;\,B} \right)\,\,\)

\(Y\,\, = \,\,\left( {\overline A \,\, + \;\,\overline B } \right)\,\,.\,\,\left( {A\,\, + \;\,B} \right)\)

\(Y\,\, = \,\,\overline A .\,\,A\,\, + \;\,\overline A .\,B\,\, + \,\,\overline B .\,A\,\, + \;\,\overline B \,.\,\,B\,\,\)

\(Y\,\, = \,\,\overline A .\,B\,\, + \;\,A.\,\overline B \,\,\,\,\)

જ્યારે \(A\,\, = \,\,1,\,\,B\,\, = \,\,0\) ત્યારે \(Y\,\, = \,\,\overline 1 \,.0\,\, + \;\,1.\overline 0 \,\, = \,\,0.0\,\, + \;\,1.1\,\, = \,\,1\)

જ્યારે \(A\,\, = \,\,1,\,\,\,B\, = \,\,1\,\) ત્યારે \(\,Y\,\, = \,\,\overline 1 .\,0\,\, + \;\,1\,.\,\overline 1  = \,\,0.1\,\, + \;\;1.0\,\, = \,\,0\,\, + \;\,0\,\, = \,\,0\)

જ્યારે \(A\,\, = \,\,0,\,\,B\,\, = \,\,0\,\) ત્યારે  \(Y\,\, = \,\,\overline 0 .0\,\, + \;\,0.\overline 0 \,\, = \,\,1.0\,\, + \,\,0.1\,\, = \,\,0\,\, + \;\,0\,\, = \,\,0\)