If A = {x : x ∈ ℤ, x² = 2}, what kind of set is A?
Answer and explanation
Correct answer: Empty set
Solving x² = 2 over the real numbers gives x = √2 and x = −√2. Neither value is an integer, because √2 is irrational and cannot be written as a whole-number integer. The defining condition also requires x ∈ ℤ, so no integer satisfies the equation. Therefore A has no elements and is the empty set, written as ∅.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
Solving x² = 2 over the real numbers gives x = √2 and x = −√2. Neither value is an integer, because √2 is irrational and cannot be written as a whole-number integer. The defining condition also requires x ∈ ℤ, so no integer satisfies the equation. Therefore A has no elements and is the empty set, written as ∅.
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.
