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In this Class 11 Mathematics topic from the Sets chapter, students learn how to represent a set in roster form when its elements are defined by inequalities. They practise interpreting conditions such as x < 5 or 2 ≤ x ≤ 6, identifying the appropriate number system, and listing every element clearly within braces. The topic also strengthens understanding of finite sets, endpoints, and the difference between a rule that defines a set and its explicit roster representation.
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Easy · Level 1 · sets,roster form,inequalities,set-builder notation,Roster form with inequalities,Mathematics,Class 11 MCQView options
B = {8, 9, 10, 11}
B = {9, 10}
B = {8, 9, 10}
B = {9, 10, 11}
Easy · Level 1 · sets,strict inequalities,roster form,Mathematics,Roster form with inequalities,Class 11 MCQView options
I = {13, 14, 15}
I = {12, 13, 14, 15, 16}
I = {12, 13, 14, 15}
I = {13, 14, 15, 16}
Question 1EasyLevel 1
What is the roster form of B = {x : x is a natural number and 8 ≤ x ≤ 11}?
Correct answer: A
The governing concept is converting set-builder notation into roster form by listing every value that satisfies the stated condition. Both inequalities use the symbol ≤, so the endpoints 8 and 11 are included. The natural numbers from 8 through 11 are 8, 9, 10, and 11; hence B = {8, 9, 10, 11}, making option A correct. Option C excludes the upper endpoint 11, while option D excludes the lower endpoint 8. Option B excludes both endpoints and therefore contains only the interior values. The order of elements in a set does not matter, but increasing order makes the complete list easy to verify.
What is the roster form of I = {x : x is a natural number and 12 < x < 16}?
Correct answer: A
The governing concept is converting strict inequalities into a roster of qualifying natural numbers. The condition 12 < x means x must be greater than 12, while x < 16 means it must be less than 16. Because both signs are strict, neither endpoint 12 nor endpoint 16 is included. The natural numbers strictly between them are 13, 14, and 15. Therefore I = {13, 14, 15}, making option A correct. Option B includes both forbidden endpoints, option C includes 12, and option D includes 16. The answer demonstrates the difference between strict signs (<) and inclusive signs (≤), which is essential when forming a finite roster.
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