If A = {x ∈ ℤ : x² = 49 and x < 0} and B = {−7}, which statement is correct?
Answer and explanation
Correct answer: A = B;
To determine A, solve x² = 49. The integer solutions are x = 7 and x = −7. The additional condition x < 0 excludes 7 and retains only −7, so A = {−7}. Since B is also defined as the singleton set {−7}, A and B contain exactly the same element. Therefore, A = B. The braces show that each is a set, not merely the number −7.
Frequently asked questions
What is the correct answer to this question?
A = B;
Why is this the correct answer?
To determine A, solve x² = 49. The integer solutions are x = 7 and x = −7. The additional condition x < 0 excludes 7 and retains only −7, so A = {−7}. Since B is also defined as the singleton set {−7}, A and B contain exactly the same element. Therefore, A = B. The braces show that each is a set, not merely the number −7.
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.
