If L₁ = {x : x ∈ ℕ, x² < 10} and M₁ = {1, 2, 3}, is L₁ = M₁?
Answer and explanation
Correct answer: Yes, because both have the same elements
Since x belongs to the natural numbers and x² < 10, test the natural numbers in order: 1² = 1, 2² = 4, and 3² = 9, all of which are less than 10. However, 4² = 16, so 4 is excluded. Therefore L₁ = {1, 2, 3}, which is exactly M₁. Two sets are equal when they contain precisely the same elements, regardless of how those elements are written or listed.
Frequently asked questions
What is the correct answer to this question?
Yes, because both have the same elements
Why is this the correct answer?
Since x belongs to the natural numbers and x² < 10, test the natural numbers in order: 1² = 1, 2² = 4, and 3² = 9, all of which are less than 10. However, 4² = 16, so 4 is excluded. Therefore L₁ = {1, 2, 3}, which is exactly M₁. Two sets are equal when they contain precisely the same elements, regardless of how those elements are written or listed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
