Let \(A=\{x:x\text{ is a positive even divisor of }18\}\) and \(B=\{2,6,18\}\). Which statement is true?
Answer and explanation
Correct answer: \(A=B\)
The positive divisors of 18 are 1, 2, 3, 6, 9, and 18. Among them, the even divisors are 2, 6, and 18, because each is divisible by 2. Therefore, \(A=\{2,6,18\}\), which is exactly the set \(B\). The claim that 18 is not even is false, since 18 is divisible by 2. Hence \(A=B\), and option B is correct.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The positive divisors of 18 are 1, 2, 3, 6, 9, and 18. Among them, the even divisors are 2, 6, and 18, because each is divisible by 2. Therefore, \(A=\{2,6,18\}\), which is exactly the set \(B\). The claim that 18 is not even is false, since 18 is divisible by 2. Hence \(A=B\), and option B is correct.
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.
