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What is the correct result of \( (-\infty,1] \cap (-4,6) \) on the number line?संख्या रेखा पर \( (-\infty,1] \cap (-4,6) \) का सही परिणाम क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \( (-4,1] \)\( (-4,1] \)
The intersection \( (-\infty,1] \cap (-4,6) \) keeps only the numbers that satisfy both conditions. From \( (-\infty,1] \), we have \(x\le 1\). From \( (-4,6) \), we have \( -4<x<6\). Combining gives \( -4<x\le 1\), which in interval notation is \( (-4,1] \).\( (-\infty,1] \cap (-4,6) \) का प्रतिच्छेद वही संख्याएँ देता है जो दोनों शर्तें पूरी करती हैं। \( (-\infty,1] \) से \(x\le 1\) मिलता है। \( (-4,6) \) से \( -4<x<6\) मिलता है। दोनों को मिलाने पर \( -4<x\le 1\) प्राप्त होता है, जिसे अंतराल रूप में \( (-4,1] \) लिखा जाता है।
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