$($Only answer part $2$ and $3)$Consider two discrete memoryless channels $($DMCs$),((x_1|))$ and $((x_2|)),$ with capacities $C_1$ and $C_2,$ respectively. A new channel $(x_1((x_2|)|))$ is formed in which $x_{1}in{x}_1$ and $x_{2}in{x}_2$ are sent simultaneously, resulting in $y_1,y_2.$

Find the capacity of this channel.

Having the codebook of each channel, create a codebook for the joint channel that achieves the capacity.

What if we are only allowed to use one channel at a time?