Question
एक उचित प्रति-उदाहरण देते हुए निम्नलिखित कथन को असिद्ध कीजिए :
ग) समुच्चय का उच्चक और निम्नक ज्ञात कीजिए।
Answer :
Word Count : 161
कथन $(x+y)^n = x^n + y^n \ \forall n \in \mathbb{N}, x, y \in \mathbb{Z}$ असिद्ध है। इसे एक सरल प्रति-उदाहरण से दिखाया जा सकता है। मान लें $x=1, y=1, n=2$। बाएँ ______ _______ ____ _____ _____ ___ ___.
______ ____ ___ ___ __________ ___ _________ ___ ________ _______ _____ ___.
____ _________ _____ __________ ____ ______ __________ ______ __________ _____ _______.
__________ _____ ______ ___ ____ __________ _______ _________ ____ ________ ________.
_______ ________ ________ ______ __________ _________ __________.
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_______ ___ ____ ___ ________ _________ ______ ___ ____ _________.
_________ _________ ______ _______ _______ _______ ____ ______ _________ _____.
______ ______ ___ __________ _________ _______ _____.
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_______ __________ __________ _________ __________ ___ _____ _________ _________ ________.
_________ ___ _________ _________ _____ _____ _____ __________ ________.
________ __________ _____ __________ ____ ___ _________ ___ ____ ______ __________.
________ __________.
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कथन $(x+y)^n = x^n + y^n \ \forall n \in \mathbb{N}, x, y \in \mathbb{Z}$ असिद्ध है। इसे एक सरल प्रति-उदाहरण से दिखाया जा सकता है। मान लें $x=1, y=1, n=2$। बाएँ ______ _______ ____ _____ _____ ___ ___.
______ ____ ___ ___ __________ ___ _________ ___ ________ _______ _____ ___.
____ _________ _____ __________ ____ ______ __________ ______ __________ _____ _______.
__________ _____ ______ ___ ____ __________ _______ _________ ____ ________ ________.
_______ ________ ________ ______ __________ _________ __________.
______ ____ ______ _____ _____.
__________ _____ ________ ____ _____ ______ _____ ______ ____ ________ ____.
_______ ___ ____ ___ ________ _________ ______ ___ ____ _________.
_________ _________ ______ _______ _______ _______ ____ ______ _________ _____.
______ ______ ___ __________ _________ _______ _____.
____ __________ ___ ___ __________ ________.
_______ __________ __________ _________ __________ ___ _____ _________ _________ ________.
_________ ___ _________ _________ _____ _____ _____ __________ ________.
________ __________ _____ __________ ____ ___ _________ ___ ____ ______ __________.
________ __________.
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