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In this Class 11 Mathematics topic from Sets, students learn to express a set in roster form by listing all its distinct elements inside braces. They use factor-based conditions to identify the required elements, such as the positive factors of a number, and check that no element is omitted or repeated. The topic also reinforces that the order of elements does not change a set and helps students move accurately from a verbal or symbolic description to an explicit list.
TOPIC PRACTICE
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Easy · Level 1View options
Positive factors of 6
Multiples of 6
Even numbers less than 6
Odd numbers less than 6
Easy · Level 1View options
A = {1, 2, 4, 8, 16}
A = {2, 4, 6, 8, 10, 12, 14, 16}
A = {16, 32, 48}
A = {1, 4, 16}
Question 1EasyLevel 1
If L = {1, 2, 3, 6}, which is the correct description of L?
Correct answer: A
The governing concept is distinguishing factors from multiples. A positive factor of 6 is a positive whole number that divides 6 exactly, leaving remainder zero. The divisions 6 ÷ 1 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2, and 6 ÷ 6 = 1 show that 1, 2, 3, and 6 are precisely the positive factors of 6. Therefore option A is correct. Multiples of 6 would include 6, 12, 18, and so on, so option B does not match. Even numbers less than 6 are 2 and 4, while odd numbers less than 6 are 1, 3, and 5. Neither option C nor D gives exactly the listed set.
Which option is the roster form of A = {x : x is a positive factor of 16}?
Correct answer: A
The governing concept is writing a set in roster form by listing every positive factor that divides 16 exactly. Testing the divisors gives 16 ÷ 1 = 16, 16 ÷ 2 = 8, 16 ÷ 4 = 4, 16 ÷ 8 = 2, and 16 ÷ 16 = 1, all with no remainder. Thus the complete set of positive factors is {1, 2, 4, 8, 16}. Option B contains numbers such as 6, 10, 12, and 14 that do not divide 16 exactly. Option C lists multiples of 16 rather than factors, and option D omits 2 and 8. Therefore option A lists all and only the required factors.
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