If A = {0, 1} and B = {x : x² = x}, what is the correct relation between A and B?
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Answer and explanation
Correct answer: A = B
To determine B, solve x² = x. Rearranging gives x² − x = 0, or x(x − 1) = 0. Hence x = 0 or x = 1, so B = {0,1}. Since A also contains exactly 0 and 1, the two sets have identical elements and are equal. Thus A = B. The other choices wrongly describe a proper subset, omit 0, or claim that the intersection is empty.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
To determine B, solve x² = x. Rearranging gives x² − x = 0, or x(x − 1) = 0. Hence x = 0 or x = 1, so B = {0,1}. Since A also contains exactly 0 and 1, the two sets have identical elements and are equal. Thus A = B. The other choices wrongly describe a proper subset, omit 0, or claim that the intersection is empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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