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Asked by Rajitha Last Modified
Answer As a seasoned tutor registered on UrbanPro, I'm glad to assist you with this question. UrbanPro is indeed a fantastic platform for online coaching and tuition, providing a conducive environment for both tutors and students to engage in effective learning experiences.
Let's tackle the given sets and operations:
Given:
(i) We need to find A′ ∪ (B ∩ C′)
To find A′ (complement of A), we need to consider all the elements in U that are not in A: A′ = {1, 3, 5, 7}
Next, let's find C′ (complement of C), which includes all elements in U that are not in C: C′ = {3, 5, 6}
Now, we need to find the intersection of B and C′: B ∩ C′ = {5}
Finally, we take the union of A′ and (B ∩ C′): A′ ∪ (B ∩ C′) = {1, 3, 5, 7} ∪ {5} = {1, 3, 5, 7}
(ii) We need to find (B – A) ∪ (A – C)
First, let's find (B – A), which means elements in B that are not in A: B – A = {3, 5}
Next, let's find (A – C), which means elements in A that are not in C: A – C = {6}
Now, we take the union of (B – A) and (A – C): (B – A) ∪ (A – C) = {3, 5} ∪ {6} = {3, 5, 6}
So, the solutions are: (i) A′ ∪ (B ∩ C′) = {1, 3, 5, 7} (ii) (B – A) ∪ (A – C) = {3, 5, 6}
If you have any further questions or need clarification, feel free to ask!
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