Question
Download Solution PDFदो समुच्चय A = {1, 2, 7, 9, 12} और B = {x : x2 - 10x + 16 = 0} का संश्रय क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
समुच्चयों का संश्रय:
माना कि A और B दो समुच्चय है।
A और B का संश्रय उन सभी तत्वों का समुच्चय होता है जो या तो A या B या A और B दोनों से संबंधित है।
A और B के संश्रय को A ∪ B द्वारा दर्शाया गया है।
अर्थात् A ∪ B = {x : x ∈ A या x ∈ B}
किसी दो समुच्चयों के संश्रय के लिए वेंन आरेख को नीचे दर्शाया गया है:
गणना:
समुच्चय A = {1, 2, 7, 9, 12}
x2 - 10x + 16 = 0
x2 - 2x - 8x + 16 = 0
(x - 2)(x - 8) = 0
x = 2, 8
समुच्चय B = {2, 8}
∴ समुच्चय (A ∪ B) = {1, 2, 7, 8, 9, 12}
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