please someone else answer it

Q1.Suppose Alice, Bob, and Carol want to use the secret key technology to authenticate each other. If they all used the same secret key K, then Bob could impersonate Carol to Alice (actually any of the three could impersonate another to the third). Suppose instead that each had their own secret key: Alice uses Ka, Bib uses Kb, and Carol uses Kc. This means that, to prove his or her identity, each one responds to a challenge with a function of his or her secret key and the challenge. Is this more secure than having them all use the same secret key (K)?