Since P(X*X) is a power set of X*X, the elements of P(X*X) are all subsets of X*X, or P(X*X) is a set of all relations on x, the relations on x satisfy the binding property for compound operation, and the identity relation is a unary about compound operation, so (P(X*X),? ) is a semigroup, but any relation r on x does not necessarily have an inverse, that is, the relation r does not necessarily have a q, so RQ=QR=I, where I is an identity relation on x, and if an empty relation does not have an inverse, then it is definitely not just an empty relation. So what you feel is right, but what the textbook says is wrong.