If A is the set of natural-number divisors common to 12 and 18, and B = {1, 2, 3, 6}, which statement is correct?
Answer and explanation
Correct answer: A = B
The governing concept is finding common elements of two divisor sets and then comparing sets. The positive divisors of 12 are 1, 2, 3, 4, 6, and 12, while those of 18 are 1, 2, 3, 6, 9, and 18. Their common divisors are therefore 1, 2, 3, and 6. Thus A = {1, 2, 3, 6}, exactly the same elements as B. Option B lists only one common divisor, option C includes non-common divisors, and option D is false.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The governing concept is finding common elements of two divisor sets and then comparing sets. The positive divisors of 12 are 1, 2, 3, 4, 6, and 12, while those of 18 are 1, 2, 3, 6, 9, and 18. Their common divisors are therefore 1, 2, 3, and 6. Thus A = {1, 2, 3, 6}, exactly the same elements as B. Option B lists only one common divisor, option C includes non-common divisors, and option D is false.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
