The correct answer is: Only assumption II is implicit.
The statement “Why don’t you invite Anthony for the Christmas party this year?” does not provide enough information to determine whether or not Anthony is from the same city. It is possible that Anthony is from the same city and that the speaker simply does not know him well enough to invite him. However, it is also possible that Anthony is not from the same city and that the speaker is aware of this fact.
The statement does provide some evidence to support the assumption that unless invited, Anthony will not attend the party. The speaker is asking why Anthony has not been invited, which suggests that the speaker believes that Anthony would attend if he were invited. However, the statement does not provide any definitive proof that Anthony would attend if he were invited.
Therefore, the only assumption that is implicit in the statement is assumption II.