Question $4(20$ polmis$)$ of $\backslash ($ Q $\backslash )$ to inves in the projects. Projects are bake$-$ti or leave$-$it lype of projects. Yos are net allowed the constraints to inpoge the following addacional requirements. You can define ablitional variaties if you want. Please provide definition of the additional variables defined

$($a$)(5$ points$)$ Either both projects I and $5$ are chosen or neither are ehosen.

$($b$)(5$ points$)$ Neither project $5$ mor $6$ can be chosen unless either $3$ or $4$ is chosen.

$($c$)(5$ points$)$ At least two of the projects $1,2,3$ are chosen, or at most three of the projects $4,5,6,7,8$ are chosen.

$($d$)(5$ points$)$ If both projects $1$ and $2$ are chosen, then at least one of projects $9$ and $10$ should also be chosen.