IV$.($@$3$ pts$,{24}^{46}$ total points$)$ The following questions refer to a capital budgeting problem of six projects represented by $0-1$ variables $x_1,x_2,x_3,x_4,x_5$ and $x_4$ such that

$x=1$ if project i is selected,

$x_C=0$ if project $i$ is not selected.

$i=1,2,3,4,5,6$

Write a constraint $($or constraints$)$ to represent each restriction below $($assuming that each situation is not related to the others$).$ For each item, your constraint$($s$)$ should reflect the restriction exactly, no more no less.

$($a$)$ It is not allowed to select all of the six projects.

$($b$)$ At least two of the projects $2,3,4$ and $5$ must be selected.

$($c$)$ Project $1$ and project $6$ must be selected or deselected simultancously.

$($d$)$ Between project $2$ and project $5,$ one must be selected, but not both.