Eileen is having a party and finds herself confronted with decisions about inviting five of her friends.

a. If she invites Margaret, she must also invite Joan.

b. If Kathleen is invited, Nettie and Margaret must also be invited.

c. She can invite Cathy or Joan, but definitely not both of them.

d. Neither Cathy nor Nettie will show up if the other is not invited.

e. Either Kathleen or Nettie or both must be invited.

Determine which subsets of these five friends Eileen can invite to her party and still satisfy conditions (a) through (e).