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The statement (x^2\ge x) is not true for all (x\in\mathbb{R}). Which value is a counterexample?कथन (x^2\ge x) सभी (x\in\mathbb{R}) के लिए सत्य नहीं है। कौन सा मान इसका प्रतिउदाहरण है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (x=\frac{1}{2})(x=\frac{1}{2})
At (x=\frac{1}{2}), (x^2=\frac{1}{4}), which is less than (\frac{1}{2}). One counterexample is enough to disprove a universal statement.(x=\frac{1}{2}) पर (x^2=\frac{1}{4}), जो (\frac{1}{2}) से छोटा है। सार्वत्रिक कथन को गलत करने के लिए एक प्रतिउदाहरण काफी है।
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