If A = {x : x ∈ ℤ, x² = 9} and B = {-3, 3}, which statement is correct?
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Answer and explanation
Correct answer: A = B
The condition x² = 9 means x² − 9 = 0, which factors as (x − 3)(x + 3) = 0. Thus the integer solutions are x = 3 and x = −3, so A = {-3, 3}. Since B is also defined as {-3, 3}, both sets contain exactly the same elements and therefore A = B. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The condition x² = 9 means x² − 9 = 0, which factors as (x − 3)(x + 3) = 0. Thus the integer solutions are x = 3 and x = −3, so A = {-3, 3}. Since B is also defined as {-3, 3}, both sets contain exactly the same elements and therefore A = B. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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