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Asked by Divya Last Modified
Answer As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best online coaching tuition platforms available for students seeking academic assistance. Now, let's tackle your set theory problem using the given sets U, A, and B.
Given: U = {1, 2, 3, 4, 5, 6} A = {2, 3} B = {3, 4, 5}
First, let's find the complements of sets A and B: A′ (complement of A) = {1, 4, 5, 6} (Elements in U but not in A) B′ (complement of B) = {1, 2, 6} (Elements in U but not in B)
Now, let's find the intersection of the complements of A and B: A′ ∩ B′ = {1, 6} (Elements common to both A′ and B′)
Next, let's find the union of sets A and B: A ∪ B = {2, 3, 4, 5} (All elements in both A and B without repetition)
Finally, let's find the complement of the union of sets A and B: (A ∪ B)′ (complement of A ∪ B) = {1, 6} (Elements in U but not in A ∪ B)
We've shown that A′ ∩ B′ = (A ∪ B)′, which demonstrates De Morgan's Law for sets.
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