If \(A=\{x\mid x\) is a prime divisor of 30\} and \(B=\{2,3,5\}\), what is the relation between \(A\) and \(B\)?
Answer and explanation
Correct answer: \(A=B\)
The prime factorization of 30 is \(30=2\times3\times5\). Therefore its prime divisors are exactly 2, 3, and 5, so \(A=\{2,3,5\}\). This is the same set as \(B\), which means \(A=B\), not merely a proper subset. The numbers 1 and 30 are not prime numbers, so option D is also incorrect. Hence option A gives the correct relation.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The prime factorization of 30 is \(30=2\times3\times5\). Therefore its prime divisors are exactly 2, 3, and 5, so \(A=\{2,3,5\}\). This is the same set as \(B\), which means \(A=B\), not merely a proper subset. The numbers 1 and 30 are not prime numbers, so option D is also incorrect. Hence option A gives the correct relation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
