If E₁ = {x : x ∈ ℕ and 5 ≤ x ≤ 5}, what type of set is E₁?
Answer and explanation
Correct answer: Singleton set
The two inequalities 5 ≤ x and x ≤ 5 together force x to be exactly 5. Therefore, E₁ = {5}, which contains precisely one element. A set containing exactly one element is called a singleton set. It is also finite, but the most specific answer among the choices is singleton set. It cannot be empty because 5 satisfies the condition, and it cannot be infinite because there is only one permitted value.
Frequently asked questions
What is the correct answer to this question?
Singleton set
Why is this the correct answer?
The two inequalities 5 ≤ x and x ≤ 5 together force x to be exactly 5. Therefore, E₁ = {5}, which contains precisely one element. A set containing exactly one element is called a singleton set. It is also finite, but the most specific answer among the choices is singleton set. It cannot be empty because 5 satisfies the condition, and it cannot be infinite because there is only one permitted value.
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.
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