Question
Download Solution PDFमाना A और B दो ऐसे समुच्चय हैं जिनके लिए n(A - B) = 20 + x, n(B - A) = 3x और n(A ∩ B) = x + 1 है। यदि n(A) = n(B) है, तो (2x - 5) का मान ज्ञात कीजिए:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
n(A - B) = 20 + x
n(B - A) = 3x
n(A ∩ B) = x + 1
n(A) = n(B)
प्रयुक्त सूत्र:
समुच्चय A में कुल अवयव: n(A) = n(A - B) + n(A ∩ B)
समुच्चय B में कुल अवयव: n(B) = n(B - A) + n(A ∩ B)
चूँकि n(A) = n(B) है, इसलिए हम व्यंजकों को समान करते हैं।
गणना:
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
चूँकि n(A) = n(B):
⇒ 21 + 2x = 4x + 1
⇒ 21 - 1 = 4x - 2x
⇒ 20 = 2x
⇒ x = 10
हमें (2x - 5) का मान ज्ञात करना है:
⇒ (2 × 10 - 5) = 20 - 5
⇒ 15
∴ सही उत्तर विकल्प (4) है।
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