What is correct about the statement [2,4] ⊆ (2,4)?
Answer and explanation
Correct answer: It is false because 2 and 4 are not in the open interval
The closed interval [2,4] contains every real number from 2 through 4, including both endpoints 2 and 4. The open interval (2,4) contains only numbers strictly greater than 2 and strictly less than 4, so it excludes both endpoints. Since 2 and 4 belong to the first set but not the second, [2,4] is not a subset of (2,4). One counterexample is enough to disprove a subset statement.
Frequently asked questions
What is the correct answer to this question?
It is false because 2 and 4 are not in the open interval
Why is this the correct answer?
The closed interval [2,4] contains every real number from 2 through 4, including both endpoints 2 and 4. The open interval (2,4) contains only numbers strictly greater than 2 and strictly less than 4, so it excludes both endpoints. Since 2 and 4 belong to the first set but not the second, [2,4] is not a subset of (2,4). One counterexample is enough to disprove a subset statement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
