Which statement is correct about X={x∈Z: x²=4} and Y={-2,2}?
Answer and explanation
Correct answer: X=Y
The governing concept is equality of sets: two sets are equal when they contain exactly the same elements, regardless of order. Solving x²=4 over the integers gives x=2 or x=-2, since 2²=4 and (-2)²=4. Therefore X={-2,2}, which has precisely the same members as Y={-2,2}. Thus X=Y, so option A is correct; X is not just {2}, and Y contains no 4.
Frequently asked questions
What is the correct answer to this question?
X=Y
Why is this the correct answer?
The governing concept is equality of sets: two sets are equal when they contain exactly the same elements, regardless of order. Solving x²=4 over the integers gives x=2 or x=-2, since 2²=4 and (-2)²=4. Therefore X={-2,2}, which has precisely the same members as Y={-2,2}. Thus X=Y, so option A is correct; X is not just {2}, and Y contains no 4.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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