GATE 2016 EE -SET 2 Question 26

$$\overline{(a+\bar{b}+c+\bar{d})+(b+\bar{c})}$$ =$$\overline{a+\bar{b}+c+\bar{d}}\cdot \overline{b+\bar{c}}$$

$$\left [ \because \overline{a+b}=\bar{a}\cdot \bar{b} \right ]$$ de Morgan’s theorem.

$$\Rightarrow (\bar{a}\cdot b\cdot \bar{c}\cdot d)(\bar{b}\cdot c)=0$$