Problem $2(10$ Points, $2\mathrm{.}5$ points each, $-1\mathrm{.}25$ per error$)$

You have a set of $15$ potential projects from which you must select a subset of projects. We will use binary variables X$1...$ X$15,$ where if a project is selected, then its corresponding variable $=1,0$ otherwise. Formulate each of the four constraints below and ensure that you show your work and list your variables in the correct order. Note: You do not need to define the variables or the objective function for this problem.

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Constraint $1)$ Project $14$ could be selected if and only if all of Project $1,$ Project $2,$ & Project $9$ are selected.

Constraint $2)$ Project $15$ must be selected if Project $5$ is selected. Project $5$ must be selected if Project $15$ is selected.

Constraint $3)$ Project $13$ must be selected if Project $8$ is selected. The reverse is not true.

Constraint $4)$ Project $11$ must be selected if all of Projects $1,2,3,4,5,6,$ & $7$ are selected.