Consider the following statements with reference to the events A, B, C: I. (A∪B∪C)∩(Ā∩B̄∩C̄) is an impossible event. II. (A∩B∩C)∩(Ā∪B̄∪C̄) is a possible event. Which of the statements given above is/are correct?

Statement I: (A∪B∪C) means at least one of A,B,C occurs; (Ā∩B̄∩C̄) means none of A,B,C occurs. These are complementary, so their intersection is empty (impossible event). Statement I is correct. Statement II: (A∩B∩C) means all three occur; (Ā∪B̄∪C̄) means at least one does NOT occur. These are complementary (by De Morgan: Ā∪B̄∪C̄ = complement of A∩B∩C). So intersection is empty (impossible event), not possible. Statement II is incorrect.