If X₁ = {x : x ∈ ℤ, x² = 25} and Y₁ = {5, −5, 5}, which statement is correct?
Answer and explanation
Correct answer: X₁ = Y₁
The integer solutions of x² = 25 are x = 5 and x = −5, so X₁ = {5, −5}. In set notation, repeating an element does not create a new element; duplicates are ignored. Therefore Y₁ = {5, −5, 5} represents the same set as {5, −5}. Both sets contain exactly the two elements 5 and −5, so X₁ = Y₁. Statement A is correct.
Frequently asked questions
What is the correct answer to this question?
X₁ = Y₁
Why is this the correct answer?
The integer solutions of x² = 25 are x = 5 and x = −5, so X₁ = {5, −5}. In set notation, repeating an element does not create a new element; duplicates are ignored. Therefore Y₁ = {5, −5, 5} represents the same set as {5, −5}. Both sets contain exactly the two elements 5 and −5, so X₁ = Y₁. Statement A is correct.
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.
