If \(A=\{x:x\text{ is a prime factor of }12\}\) and \(B=\{2,3\}\), which statement is true?
Answer and explanation
Correct answer: \(A=B\)
The prime factorization of 12 is \(12=2^2\times3\). Its distinct prime factors are therefore 2 and 3. A set does not record multiplicity, so the repeated factor 2 is listed only once; we do not write \(\{2,2,3\}\). Hence \(A=\{2,3\}=B\). Option C is false because equal sets are not proper subsets of one another, and option D is false because 12 is not an element of either set.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The prime factorization of 12 is \(12=2^2\times3\). Its distinct prime factors are therefore 2 and 3. A set does not record multiplicity, so the repeated factor 2 is listed only once; we do not write \(\{2,2,3\}\). Hence \(A=\{2,3\}=B\). Option C is false because equal sets are not proper subsets of one another, and option D is false because 12 is not an element of either set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
