Can you help me with number $1,2,$ and $3$ please? Thank you

$1.$ A vertex cover of an undirected graph is a set of vertices of such that every edge of the graph has an endpoint in the set. For example, in the graph below, $\backslash (\backslash \{2,4,6\backslash \}\backslash )$ is a vertex cover because every edge has an endpoint in $\backslash (\backslash \{2,4,6\backslash \}\backslash ).$

Given an undirected graph $\backslash ($ G $\backslash ),$ formulate an integer program which finds a vertex cover of minimum size. $($The info you are given is the set of vertices and the set of edges of the graph, and your IP will depend on this information. You do not need to code your IP$.)$

$2.$ A clique of an undirected graph is a set of vertices such that any two vertices in the set are adjacent to each other. For example, in the above graph, $\backslash (\backslash \{1,2,4,6\backslash \}\backslash )$ and $\backslash (\backslash \{2,5,6\backslash \}\backslash )$ are cliques.

Given an undirected graph $\backslash ($ G $\backslash ),$ formulate an integer program which finds a clique of $\backslash ($ G $\backslash )$ of maximum size.

$3.$ Consider the LP relaxation of your IP from problem $1.$ Show that for the below graph, the LP relaxation gives a different optimal value than the IP$.$ Do the same for your IP from problem $2.$