Which statement is true?
Answer and explanation
Correct answer: (0, 1) ⊆ (0, 2)
Every number x in the open interval (0, 1) satisfies 0 < x < 1. Since every such number is also less than 2, it satisfies 0 < x < 2 and therefore belongs to (0, 2). Hence (0, 1) is a subset of (0, 2). The reverse inclusion is false because numbers such as 1.5 belong to (0, 2) but not to (0, 1); the intervals are not equal. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
(0, 1) ⊆ (0, 2)
Why is this the correct answer?
Every number x in the open interval (0, 1) satisfies 0 < x < 1. Since every such number is also less than 2, it satisfies 0 < x < 2 and therefore belongs to (0, 2). Hence (0, 1) is a subset of (0, 2). The reverse inclusion is false because numbers such as 1.5 belong to (0, 2) but not to (0, 1); the intervals are not equal. 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.
