If A is the set of prime divisors of 42 and B = {2, 3, 7}, which statement is correct?
Answer and explanation
Correct answer: A = B
Prime divisors are prime numbers that divide the given number exactly. The prime factorization of 42 is 42 = 2 × 3 × 7. Therefore, the complete set of prime divisors of 42 is A = {2, 3, 7}. This is exactly the set specified as B, so A = B. Options B and C are incorrect because equal sets are not proper subsets of one another. Option D is false because A contains three elements and is therefore not empty.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Prime divisors are prime numbers that divide the given number exactly. The prime factorization of 42 is 42 = 2 × 3 × 7. Therefore, the complete set of prime divisors of 42 is A = {2, 3, 7}. This is exactly the set specified as B, so A = B. Options B and C are incorrect because equal sets are not proper subsets of one another. Option D is false because A contains three elements and is therefore not empty.
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.
