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What is the result of \( (-\infty,6] \setminus (1,6] \) on the number line?संख्या रेखा पर \( (-\infty,6] \setminus (1,6] \) का परिणाम क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \( (-\infty,1] \)\( (-\infty,1] \)
The expression \( A\setminus B \) means elements in \(A\) that are not in \(B\). Here \(A=(-\infty,6] \) and \(B=(1,6]\). So we remove all numbers greater than \(1\) up to \(6\), including \(6\). Therefore all numbers \(x\le 1\) remain. Hence the result is \( (-\infty,1] \).\( A\setminus B \) का अर्थ है \(A\) में मौजूद वे तत्त्व जो \(B\) में नहीं हैं। यहाँ \(A=(-\infty,6] \) और \(B=(1,6]\)। इसलिए \(1\) से बड़े और \(6\) तक के सभी मान (\(6\) सहित) हट जाएँगे। तब \(x\le 1\) वाले सभी मान बने रहते हैं। अतः परिणाम \( (-\infty,1] \) है।
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