Question

Dual of$(x\vee y)\wedge (x\vee 1)=x\vee (x\wedge y)\vee y$ is

• A. $(x.y)+(x.0)=x.(x+y).y$
• B. $(x+y)+(x.1)=x.(x+y).y$
• C. $(x.y)(x.1)=x.(x+y).y$
• D. None of these

Answer 1

The correct option is A

$(x.y)+(x.0)=x.(x+y).y$

Replace$\mathbf{\text{'}}\mathbf{\vee }\mathbf{\text{'}}$ by$\text{'}+\text{'}$ and$\mathbf{\text{'}}\mathbf{\wedge }\mathbf{\text{'}}$ by$\text{'}.\text{'}$.

$(x+y).(x+1)=x+(x.y)+y$

Dual of$\mathbf{(}\mathit{x}\mathbf{+}\mathit{y}\mathbf{)}\mathbf{.}\mathbf{(}\mathit{x}\mathbf{+}\mathbf{1}\mathbf{)}\mathbf{=}\mathit{x}\mathbf{+}\mathbf{(}\mathit{x}\mathbf{.}\mathit{y}\mathbf{)}\mathbf{+}\mathit{y}$ is written by replacing$\text{'}+\text{'}$ to$\text{'}.\text{'}$ and$\text{'}1\text{'}$ to$\text{'}0\text{'}$ and vice versa

Dual of$(x+y).(x+1)=x+(x.y)+y$ is

$(x.y)+(x.0)=x.(x+y).y$

Hence, option$\left(A\right)$ is the correct option.