Let A, B, and C be three events in a sample space . Express each of the

Let A, B, and C be three events in a sample space Ω. Express each of the following events by the use of the operators (unions, intersections, complements) among sets:

(i) all three events occur;

(ii) at least one of the three events occur;

(iii) A occurs, but not A and B;

(iv) A and C occur, but not B;
(v) at least one of the three events occur, but C does not occur;
(vi) exactly two among the three events A, B, and C occur.