Why is the statement [0, 1] ⊆ (0, 1] false?
Answer and explanation
Correct answer: Because 0 belongs to [0, 1] but not to (0, 1]
The interval [0, 1] includes both endpoints, so it contains 0 and 1. The interval (0, 1] excludes 0 because it has a round bracket at the left endpoint, but it includes 1 because it has a square bracket there. Since 0 is an element of the first interval but not of the second, the first interval cannot be a subset of the second. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
Because 0 belongs to [0, 1] but not to (0, 1]
Why is this the correct answer?
The interval [0, 1] includes both endpoints, so it contains 0 and 1. The interval (0, 1] excludes 0 because it has a round bracket at the left endpoint, but it includes 1 because it has a square bracket there. Since 0 is an element of the first interval but not of the second, the first interval cannot be a subset of the second. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
