If F = {x : x ∈ ℕ, x² < 50, and x is divisible by 3}, what is F?
Answer and explanation
Correct answer: F = {3, 6}
Because x is a positive natural number and x² < 50, we have x < √50, which is approximately 7.07. Thus the possible natural numbers are 1, 2, 3, 4, 5, 6 and 7. Among these, the numbers divisible by 3 are only 3 and 6. Therefore, the roster form of F is {3, 6}, making option A correct. Zero is excluded under the stated positive-natural-number convention, and 9 fails the square bound.
Frequently asked questions
What is the correct answer to this question?
F = {3, 6}
Why is this the correct answer?
Because x is a positive natural number and x² < 50, we have x < √50, which is approximately 7.07. Thus the possible natural numbers are 1, 2, 3, 4, 5, 6 and 7. Among these, the numbers divisible by 3 are only 3 and 6. Therefore, the roster form of F is {3, 6}, making option A correct. Zero is excluded under the stated positive-natural-number convention, and 9 fails the square bound.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
