If A = {x : x ∈ Z and x² − 2x = 0} and B = {0,2}, which statement is true?
Answer and explanation
Correct answer: A = B
Solve the defining equation: x² − 2x = x(x − 2) = 0. Therefore, x = 0 or x = 2. Both values are integers, so A = {0,2}. Since B is also defined as {0,2}, the two sets contain exactly the same elements and therefore A = B. Option B omits 0, option C incorrectly claims a proper subset relationship, and option D ignores the two valid solutions.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Solve the defining equation: x² − 2x = x(x − 2) = 0. Therefore, x = 0 or x = 2. Both values are integers, so A = {0,2}. Since B is also defined as {0,2}, the two sets contain exactly the same elements and therefore A = B. Option B omits 0, option C incorrectly claims a proper subset relationship, and option D ignores the two valid solutions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
