If V = {x : x ∈ ℕ, x² = x}, what is V?
Answer and explanation
Correct answer: V = {1}
Factor the defining equation: x² = x gives x² − x = 0, so x(x − 1) = 0. The algebraic solutions are x = 0 and x = 1. Here ℕ is taken as {1, 2, 3, ...}, so 0 is not in the stated domain. The only permitted element is 1, and therefore V = {1}. If zero were included in the convention for ℕ, option A would apply, but not under the convention used here.
Frequently asked questions
What is the correct answer to this question?
V = {1}
Why is this the correct answer?
Factor the defining equation: x² = x gives x² − x = 0, so x(x − 1) = 0. The algebraic solutions are x = 0 and x = 1. Here ℕ is taken as {1, 2, 3, ...}, so 0 is not in the stated domain. The only permitted element is 1, and therefore V = {1}. If zero were included in the convention for ℕ, option A would apply, but not under the convention used here.
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.
