Which statement is correct for (0, 1) ⊆ [0, 1]?
Answer and explanation
Correct answer: It is true because every number in (0, 1) is in [0, 1].
The statement asks whether every element of the first interval belongs to the second interval. Any x in (0, 1) satisfies 0 < x < 1, which automatically implies 0 ≤ x ≤ 1. Hence x belongs to [0, 1], and the subset statement is true. The endpoints 0 and 1 need not belong to the first interval because they are not elements of it.
Frequently asked questions
What is the correct answer to this question?
It is true because every number in (0, 1) is in [0, 1].
Why is this the correct answer?
The statement asks whether every element of the first interval belongs to the second interval. Any x in (0, 1) satisfies 0 < x < 1, which automatically implies 0 ≤ x ≤ 1. Hence x belongs to [0, 1], and the subset statement is true. The endpoints 0 and 1 need not belong to the first interval because they are not elements of it.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Linear Inequalities. Topic: representation on number line.
