If A = {x ∈ ℕ : x is a divisor of 36} and B = {1, 2, 3, 4, 6, 9, 12, 18, 36}, which option is correct about n(A) and A = B?
Answer and explanation
Correct answer: n(A) = 9 and A = B
The positive divisors of 36 can be found in pairs: 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 and 6. Removing the repeated middle entry gives the nine distinct divisors 1, 2, 3, 4, 6, 9, 12, 18, and 36. These are exactly the elements listed in B. Therefore A contains nine elements, so n(A) = 9, and because both sets have the same elements, A = B.
Frequently asked questions
What is the correct answer to this question?
n(A) = 9 and A = B
Why is this the correct answer?
The positive divisors of 36 can be found in pairs: 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 and 6. Removing the repeated middle entry gives the nine distinct divisors 1, 2, 3, 4, 6, 9, 12, 18, and 36. These are exactly the elements listed in B. Therefore A contains nine elements, so n(A) = 9, and because both sets have the same elements, A = B.
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.
