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  4. Let U be the universal set and A ∪ B ∪ C=U. Then, (A-B) ∪(B-C) ∪(C-A) prime is equal to

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Q. Let $U$ be the universal set and $A \cup B \cup C=U$. Then, $\{(A-B) \cup(B-C) \cup(C-A)\}^{\prime}$ is equal to

Sets

Solution:

It is clear from the Venn diagram,
image
$(A-B) \cup(B-C) \cup(C-A)$ represents shaded region.
$\therefore [(A-B) \cup(B-C) \cup(C-A)]^{\prime} $ represents unshaded region, which is $A \cap B \cap C$.