If A = {x : x is a positive divisor of 20} and B = {1, 2, 4, 5, 10, 20}, what is the relation between A and B?
Answer and explanation
Correct answer: A = B
A positive divisor of 20 is a positive integer that divides 20 without a remainder. The complete list is 1, 2, 4, 5, 10, and 20. Thus A = {1, 2, 4, 5, 10, 20}, which is exactly the displayed set B. Therefore A = B. The list must include both 1 and 20: 1 divides every positive integer, and every positive integer divides itself. Removing either would make the set incomplete, so option D is also incorrect.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
A positive divisor of 20 is a positive integer that divides 20 without a remainder. The complete list is 1, 2, 4, 5, 10, and 20. Thus A = {1, 2, 4, 5, 10, 20}, which is exactly the displayed set B. Therefore A = B. The list must include both 1 and 20: 1 divides every positive integer, and every positive integer divides itself. Removing either would make the set incomplete, so option D is also incorrect.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
