Question
Download Solution PDFIf A = {x: x ∈ N, x ≤ 5}, B = {x: x is prime, x < 6} and C = {x: x ∈ N, x is odd and x < 9}. Find (A ∪ B) ∩ (A ∪ C) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
Calculation:
Given: A = {x: x ∈ N, x ≤ 5}, B = {x: x is prime, x < 6} and C = {x: x ∈ N, x is odd and x < 9}
⇒ A = {1, 2, 3, 4, 5}, B = {2, 3, 5} and C = {1, 3, 5, 7}
As we know that, A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
Here, we have to find the value of (A ∪ B) ∩ (A ∪ C)
i.e we have to find the value of A ∪ (B ∩ C)
⇒ B ∩ C = {2, 3, 5} ∩ {1, 3, 5, 7} = {3, 5}
⇒ A ∪ (B ∩ C) = {1, 2, 3, 4, 5} ∪ {3, 5} = A
Hence, (A ∪ B) ∩ (A ∪ C) = {1, 2, 3, 4, 5}
Last updated on May 30, 2025
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