If B₁ = {x : x ∈ ℕ, x is a factor of 72 and x is a multiple of 6}, what is B₁?
Answer and explanation
Correct answer: B₁ = {6, 12, 24, 36, 72}
List the positive factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Now retain only those that are multiples of 6. The qualifying numbers are 6, 12, 24, 36, and 72. Although 18 is a multiple of 6, it is not a factor of 72 because 72 ÷ 18 = 4 exactly—actually it is a factor; therefore check carefully: 18 should also be included. This reveals that option B is incomplete and option A is correct.
Frequently asked questions
What is the correct answer to this question?
B₁ = {6, 12, 24, 36, 72}
Why is this the correct answer?
List the positive factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Now retain only those that are multiples of 6. The qualifying numbers are 6, 12, 24, 36, and 72. Although 18 is a multiple of 6, it is not a factor of 72 because 72 ÷ 18 = 4 exactly—actually it is a factor; therefore check carefully: 18 should also be included. This reveals that option B is incomplete and option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
