If G = {x ∈ ℕ : 3x + 1 < 16}, what is the roster form of G?
Answer and explanation
Correct answer: G = {1, 2, 3, 4}
Start with the inequality 3x + 1 < 16. Subtracting 1 from both sides gives 3x < 15, and dividing by the positive number 3 gives x < 5. Because x belongs to ℕ, using the usual school convention ℕ = {1, 2, 3, …}, the possible natural numbers less than 5 are 1, 2, 3, and 4. Therefore G = {1, 2, 3, 4}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
G = {1, 2, 3, 4}
Why is this the correct answer?
Start with the inequality 3x + 1 < 16. Subtracting 1 from both sides gives 3x < 15, and dividing by the positive number 3 gives x < 5. Because x belongs to ℕ, using the usual school convention ℕ = {1, 2, 3, …}, the possible natural numbers less than 5 are 1, 2, 3, and 4. Therefore G = {1, 2, 3, 4}, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
