Which option gives the correct statement about X={x:x∈Z, x²=16} and Y={-4,4}?
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. Solving x²=16 over the integers gives x=4 and x=-4, since both 4² and (-4)² equal 16. Therefore X={-4,4}, which is precisely Y. The negative solution must not be discarded, so option A is correct.
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. Solving x²=16 over the integers gives x=4 and x=-4, since both 4² and (-4)² equal 16. Therefore X={-4,4}, which is precisely Y. The negative solution must not be discarded, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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