Which option is the correct roster form of J₁ = {x : x ∈ ℕ, x² − 5x + 6 < 0}?
Answer and explanation
Correct answer: J₁ = ∅
Factor the quadratic: x² − 5x + 6 = (x − 2)(x − 3). This product is negative strictly between its roots, so 2 < x < 3. There is no natural number strictly between 2 and 3. The roots themselves do not qualify because the inequality is strict and gives zero at x = 2 or x = 3. Therefore, J₁ is the empty set, option A.
Frequently asked questions
What is the correct answer to this question?
J₁ = ∅
Why is this the correct answer?
Factor the quadratic: x² − 5x + 6 = (x − 2)(x − 3). This product is negative strictly between its roots, so 2 < x < 3. There is no natural number strictly between 2 and 3. The roots themselves do not qualify because the inequality is strict and gives zero at x = 2 or x = 3. Therefore, J₁ is the empty set, option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
