What type of set is A = {x ∈ ℝ : x² ≥ 0}?
Answer and explanation
Correct answer: अनंत और ℝ के बराबर
For every real number x, the square x² is always non-negative: it is positive when x is nonzero and equal to zero when x = 0. Therefore every real number satisfies x² ≥ 0. Hence A contains all real numbers and A = ℝ. Since the real-number set has infinitely many elements, A is infinite. Option A is therefore correct.
Frequently asked questions
What is the correct answer to this question?
अनंत और ℝ के बराबर
Why is this the correct answer?
For every real number x, the square x² is always non-negative: it is positive when x is nonzero and equal to zero when x = 0. Therefore every real number satisfies x² ≥ 0. Hence A contains all real numbers and A = ℝ. Since the real-number set has infinitely many elements, A is infinite. Option A is therefore correct.
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.
