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In this Class 12 Mathematics topic from the chapter Linear Inequalities, students are introduced to statements that compare quantities using symbols such as <, >, ≤ and ≥. They learn how to read and represent inequalities, distinguish them from equations, and understand how solution sets describe all values that satisfy a condition. The topic builds the foundation for solving and graphing linear inequalities on the number line.
Easy · Level 1 · 1 questions
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{x : 0 < x < 3}
{x : 0 ≤ x < 3}
{x : 0 < x ≤ 3}
{x : 0 ≤ x ≤ 3}
Question 1EasyLevel 1
Which option correctly writes the interval [0, 3) in set-builder form?अंतराल [0, 3) को समुच्चय रूप में कौन-सा विकल्प सही लिखता है?
Correct answer:सही उत्तर:B
In the interval [0, 3), the square bracket at 0 means that 0 is included, while the round parenthesis at 3 means that 3 is excluded. Therefore, the equivalent inequality is 0 ≤ x < 3. Option A excludes both endpoints, C excludes 0 and includes 3, and D includes both endpoints, so none of them represents the given interval.अंतराल [0, 3) में 0 के पास वर्ग कोष्ठक का अर्थ है कि 0 शामिल है, जबकि 3 के पास गोल कोष्ठक का अर्थ है कि 3 शामिल नहीं है। इसलिए इसका समतुल्य असमानता रूप 0 ≤ x < 3 होगा। विकल्प A दोनों सीमाएँ हटाता है, C गलत सीमा को शामिल करता है और D दोनों सीमाएँ शामिल करता है; इसलिए केवल B सही है।
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