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In the proof for (\sqrt{2}), when both (p) and (q) turn out even, which initial statement is proved false?(\sqrt{2}) के प्रमाण में (p) और (q) दोनों सम निकलने पर कौन-सा प्रारंभिक कथन झूठा सिद्ध होता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\sqrt{2}) is rational(\sqrt{2}) परिमेय है
Step 1: We initially assumed that (\sqrt{2}) is rational. Step 2: That assumption led to a common factor in a lowest-form fraction. Step 3: Therefore the initial rational assumption is proved false.चरण 1: हमने शुरुआत में (\sqrt{2}) को परिमेय माना था। चरण 2: उसी मान्यता से सरलतम भिन्न में साझा गुणनखंड आ गया। चरण 3: इसलिए प्रारंभिक परिमेय मान्यता झूठी सिद्ध होती है।
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