If W = {x : x ∈ ℝ, x² = x} and X = {0, 1}, is W = X?
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Answer and explanation
Correct answer: Yes, W and X are equal
Solve the condition defining W: x² = x gives x² − x = 0, or x(x − 1) = 0. Thus the only real solutions are x = 0 and x = 1. Consequently, W = {0, 1}. Since X is also exactly the set {0, 1}, both sets contain the same elements, so W = X. Equality of sets depends on elements, not on their order.
Frequently asked questions
What is the correct answer to this question?
Yes, W and X are equal
Why is this the correct answer?
Solve the condition defining W: x² = x gives x² − x = 0, or x(x − 1) = 0. Thus the only real solutions are x = 0 and x = 1. Consequently, W = {0, 1}. Since X is also exactly the set {0, 1}, both sets contain the same elements, so W = X. Equality of sets depends on elements, not on their order.
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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