Explanation
To evaluate the correctness of the statements, we apply De Morgan’s Laws of set theory.
Analysis of Statement I:
The expression is (A∪B∪C)∩(Aˉ∩Bˉ∩Cˉ).
According to De Morgan's Law, the complement of the union of sets is the intersection of their complements:
(Aˉ∩Bˉ∩Cˉ)=(A∪B∪C).
Substituting this into the expression:
(A∪B∪C)∩(A∪B∪C)=∅.
Since the intersection of a set and its complement is an empty set, this is an impossible event. Therefore, Statement I is correct.
Analysis of Statement II:
The expression is (A∩B∩C)∩(Aˉ∪Bˉ∪Cˉ).
According to De Morgan's Law, the complement of the intersection of sets is the union of their complements:
(Aˉ∪Bˉ∪Cˉ)=(A∩B∩C).
Substituting this into the expression:
(A∩B∩C)∩(A∩B∩C)=∅.
This also results in an empty set, which is an impossible event. Since the statement claims it is a "possible event," Statement II is incorrect.
Conclusion:
Only Statement I is correct.
Correct Option:
(a) I only
