If R₁ = {x : x ∈ ℚ, 2x + 1 = 0}, what type of set is R₁?
Answer and explanation
Correct answer: Singleton set
Solving 2x + 1 = 0 gives x = −1/2. The number −1/2 is rational because it can be expressed as a ratio of two integers with a nonzero denominator. It therefore satisfies the stated domain x ∈ ℚ. Since the equation has exactly one solution, R₁ = {−1/2} and contains one element. A set with exactly one element is called a singleton set.
Frequently asked questions
What is the correct answer to this question?
Singleton set
Why is this the correct answer?
Solving 2x + 1 = 0 gives x = −1/2. The number −1/2 is rational because it can be expressed as a ratio of two integers with a nonzero denominator. It therefore satisfies the stated domain x ∈ ℚ. Since the equation has exactly one solution, R₁ = {−1/2} and contains one element. A set with exactly one element is called a singleton set.
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.
