Question
Download Solution PDFयदि A = {1, 3, 5, 7} है, तो घांत समुच्चय P(A) की गणनीयता क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
घांत समुच्च की गणनीयता:
- एक समुच्चय की गणनीयता समुच्चय में तत्व की कुल संख्या है।
- एक घांत समुच्चय में एक समुच्चय के सभी उपसमुच्चय की सूची होती है।
- माना कि हम n तत्वों वाले एक समुच्चय A = { 1, 2, 3 .... n } को लेते हैं।
- चूँकि किसी समुच्चय के उपसमुच्चय घांत समुच्चय के अवयव होते हैं, घांत समुच्चय की गणनीयता निम्न द्वारा दी जाती है |P(A)| = 2n.
गणना:
दिया गया है: A = {1, 3, 5, 7}
- समुच्चय A में तत्वों की संख्या = 4 = n
- अब, घांत समुच्चय P(A) की गणनीयता = 2n = 24 = 16
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