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 Xi $=1$ if activity i is selected, $=0$ otherwise. Write down the following constraints:

Category Activity $($numbered$)$

Art x$1-$ Painting

x$2-$ Drawing

x$3-$ Nature craft

Music x$4-$ Rhythm band

Sports x$5-$ Relay races

x$6-$ Basketball

Computer x$7-$ Internet

x$8-$ Creative writing

x$9-$ Games

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.