If E₁ = {x : x ∈ ℤ and x² + 4 = 4}, what type of set is E₁?
Answer and explanation
Correct answer: Singleton set
Subtracting 4 from both sides of x² + 4 = 4 gives x² = 0. The only integer, and indeed the only real number, whose square is zero is x = 0. Therefore E₁ contains exactly one element: E₁ = {0}. A set with precisely one element is called a singleton set, so option B is correct; there are not two roots because +0 and −0 are the same number.
Frequently asked questions
What is the correct answer to this question?
Singleton set
Why is this the correct answer?
Subtracting 4 from both sides of x² + 4 = 4 gives x² = 0. The only integer, and indeed the only real number, whose square is zero is x = 0. Therefore E₁ contains exactly one element: E₁ = {0}. A set with precisely one element is called a singleton set, so option B is correct; there are not two roots because +0 and −0 are the same number.
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.
