Question
Download Solution PDFनिम्नलिखित में से कौन सा समुच्चय रिक्त समुच्चय है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
रिक्त समुच्चय बिना किसी तत्वों का विशिष्ट समुच्चय है; इसका आकार या गणनीयता (एक समुच्चय में तत्वों की गणना) शून्य है।
गणना:
1. x: x + 4 = 7
⇒ x = 7 - 4 = 3
∴ {x: x + 4 = 7} = {2}
यह एक रिक्त समुच्चय नहीं है।
2. {x : 7 < x < 8, x एक प्राकृतिक संख्या है} एक शून्य समुच्चय होगा क्योंकि संख्या 7 और 8 के बीच कोई प्राकृतिक संख्या नहीं है।
3. x2 - x = 2
⇒ x(x - 1) = 2
⇒ x = 2 या x = -1
∴ यह भी एक रिक्त समुच्चय नहीं है।
4. x2 - 3x + 2 = 0
⇒ x2 - 2x - x + 2 = 0
⇒ x(x - 2) - 1 (x - 2) = 0
⇒ (x- 2)(x - 1) = 0
⇒ x = 2 या x = 1
∴ यह भी एक रिक्त समुच्चय नहीं है।
इसलिए, विकल्प (2) सही है।
Last updated on Jun 20, 2025
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