If H = {x : x ∈ ℕ, 12 < x < 30, and x is divisible by 6}, then what is H?
Answer and explanation
Correct answer: H = {18, 24}
The governing concept is interpreting strict inequalities while selecting members satisfying a divisibility condition. Multiples of 6 near the interval are 12, 18, 24, and 30. Because 12 < x < 30 is strict on both sides, 12 and 30 are excluded. The remaining multiples are 18 and 24, so H = {18, 24}. Hence option B is correct; the other choices include at least one boundary value or a number below the interval.
Frequently asked questions
What is the correct answer to this question?
H = {18, 24}
Why is this the correct answer?
The governing concept is interpreting strict inequalities while selecting members satisfying a divisibility condition. Multiples of 6 near the interval are 12, 18, 24, and 30. Because 12 < x < 30 is strict on both sides, 12 and 30 are excluded. The remaining multiples are 18 and 24, so H = {18, 24}. Hence option B is correct; the other choices include at least one boundary value or a number below the interval.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
