Question
Download Solution PDFIf a set A contains 3 elements and another set B contains 6 elements, then what is the minimum number of elements that (A∪B) can have?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If A and B are two sets then, n (A ∪ B) = n (A) + n (B) - n (A ∩ B)
Calculation:
Given: n (A) = 3 and n (B) = 6.
As we know that, if A and B are two sets then, n (A ∪ B) = n (A) + n (B) - n (A ∩ B)
⇒ n (A ∪ B) = 3 + 6 - n (A ∩ B)
In order to minimize n (A ∪ B) we have to maximize n (A ∩ B) .
If A is a subset of B, then A ∩ B = A ⇒ n (A ∩ B) = n (A) = 3
⇒ n (A ∪ B) = 3 + 6 - 3 = 6.
Hence, the minimum number of elements that (A∪B) can have is 6.Last updated on May 30, 2025
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