Question
Download Solution PDFमाना कि A = {1, 3, 5}, B = {4, 6} और C = {5, 6, 7} है तो A × (B ∩ C) प्राप्त करें
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
समुच्चयों का प्रतिच्छेदन:
माना कि A और B दो समुच्चय हैं। A और B का प्रतिच्छेदन उन सभी अवयवों का समुच्चय है जो A और B दोनों समुच्चयों में मौजूद हैं।
A और B के सर्वनिष्ठ को A ∩ B द्वारा निरूपित किया जाता है
यानी A ∩ B = {x : x ∈ A और x ∈ B}
प्रतिच्छेदन के लिए वेन आरेख नीचे दिखाया गया है :
कार्टेशियन गुणनफल: A × B द्वारा निरूपित दो समुच्चय A और B का कार्टेशियन गुणनफल सभी संभव क्रमबद्ध जोड़ों का समुच्चय है जहां A के अवयव पहले और B के अवयव दूसरे हैं।
सेट-बिल्डर संकेतन में A × B = {(a, b) : a ∈ A और b ∈ B}
गणना:
दिया गया: A = {1, 3, 5}, B = {4, 6} और C = {5, 6, 7}
B ∩ C = {6}
A × (B ∩ C) = {1, 3, 5} × {6}
⇒ {(1, 6) (3, 6) (5, 6)}
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