According to the meaning of the question, C(A) represents the number of elements in non-empty set A and C(B) represents the number of elements in non-empty set B, so we can know that both set A and set B are non-empty sets, and C(A)-C(B) represent the number of elements in set A -B, so the definition of A*B is the difference between the number of elements in two sets A and B, and then take the absolute value.

Example: if A={ 1, 2,3,4}, then c (a) = 4; B={3，4，5}，C(B)= 3；

Now it is known that A*B= 1, that is, C(A)-C(B)= 1 or c (b)-c (a) =1;

There are no parameters in set A, so solve set A first, because the square of x is-1=0, so x is 1 or-1.

So the set a = {1,-1}, C(A)=2.

If C(A)-C(B)= 1, there is only one element in set b, that is, the equation in b has only one real number root.

If C(B)-C(A)= 1, there are three elements in set b, that is, the equation in b has three real roots.

This is the solution to this problem, because it is not convenient to talk about topics here. If you are not clear, please pay attention to me and I can answer your questions.

Please adopt it.