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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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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