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I enjoy logic puzzles, but not in this specific formulation.
Here, there can be several interpretations, and each has its own solution:
1) a is c - "is" means equivalence, so the other conditions are irrelevant, and if they don't contradict each other, the answer is c=a.
2) a is c - a is a part of c, meaning there exists a part of c that does not belong to a.
Therefore, the 4th condition means that the intersection of d and c is an empty set, which, according to condition 1, means that the intersection of d and a is also an empty set, which, according to condition 2, implies either:
A) a is an empty set, and the answer is "insufficient information."
B) a contradiction, and the answer is "such a situation is impossible."