If A = {x : x is a positive factor of 12} and B = {1, 2, 3, 4, 6, 12}, which statement is true?
Answer and explanation
Correct answer: A = B
The positive factors of 12 are the positive integers that divide 12 without a remainder. Checking the divisors gives 1, 2, 3, 4, 6, and 12; numbers such as 5 and 8 do not divide 12 exactly. Hence the set-builder description produces A = {1,2,3,4,6,12}, which is precisely the roster form of B. Therefore A = B. It is finite, so option D is also false, and neither proper-subset option applies.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The positive factors of 12 are the positive integers that divide 12 without a remainder. Checking the divisors gives 1, 2, 3, 4, 6, and 12; numbers such as 5 and 8 do not divide 12 exactly. Hence the set-builder description produces A = {1,2,3,4,6,12}, which is precisely the roster form of B. Therefore A = B. It is finite, so option D is also false, and neither proper-subset option applies.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
