Question
Download Solution PDFLet A and B be two sets such that n(A – B) = 20 + x, n(B – A) = 3x and n(A ∩ B) = x + 1. If n(A) = n(B), then the value of (2x – 5) is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
n(A – B) = 20 + x
n(B – A) = 3x
n(A ∩ B) = x + 1
n(A) = n(B)
Formula used:
Total elements in set A: n(A) = n(A – B) + n(A ∩ B)
Total elements in set B: n(B) = n(B – A) + n(A ∩ B)
Since n(A) = n(B), we equate the expressions.
Calculation:
n(A) = n(A – B) + n(A ∩ B)
⇒ n(A) = (20 + x) + (x + 1)
⇒ n(A) = 21 + 2x
n(B) = n(B – A) + n(A ∩ B)
⇒ n(B) = (3x) + (x + 1)
⇒ n(B) = 4x + 1
Since n(A) = n(B):
⇒ 21 + 2x = 4x + 1
⇒ 21 – 1 = 4x – 2x
⇒ 20 = 2x
⇒ x = 10
We need to find the value of (2x – 5):
⇒ (2 × 10 – 5) = 20 – 5
⇒ 15
∴ The correct answer is option (4).
Last updated on Jul 2, 2025
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