Choose the correct statement for A = {x : x² = 4, x ∈ Z} and B = {-2, 2}.
Answer and explanation
Correct answer: A = B
To find A, solve x² = 4 over the integers. Taking square roots gives x = 2 or x = -2, and both values belong to Z. Therefore A = {-2,2}. This is exactly the roster description used for B, so A = B. Option B incorrectly omits the negative solution. Option C is false because equal sets are not proper subsets of one another, and option D is false because A has two elements rather than none.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
To find A, solve x² = 4 over the integers. Taking square roots gives x = 2 or x = -2, and both values belong to Z. Therefore A = {-2,2}. This is exactly the roster description used for B, so A = B. Option B incorrectly omits the negative solution. Option C is false because equal sets are not proper subsets of one another, and option D is false because A has two elements rather than none.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
