Problem $1.$ Consider the problem faced by a summer camp recreation director who is trying to choose activities for a

rainy day. Information about possible choices is given in the table below. Let $=1$ if activity $i$ is selected, $=0$ otherwise.

Write down the following constraints:

a$.$ At least one Art activity must be done.

b$.$ If you choose the Painting activity, you cannot also choose the Drawing activity, and vice versa.

c$.$ If Basketball is chosen, then Rhythm band must also be chosen, and vice versa.

d$.$ Games can only be selected if Relay races is selected.