How can the set {x : x ∈ ℝ, x ≠ 0} be written using intervals?
Answer and explanation
Correct answer: (-∞, 0) ∪ (0, ∞)
The condition x ∈ ℝ, x ≠ 0 means that x may be any real number except zero. The negative real numbers are represented by the open interval (-∞, 0), because zero is not included. The positive real numbers are represented by (0, ∞), again with zero excluded. Combining these two disjoint parts with union gives (-∞, 0) ∪ (0, ∞). Square brackets at zero would incorrectly include zero.
Frequently asked questions
What is the correct answer to this question?
(-∞, 0) ∪ (0, ∞)
Why is this the correct answer?
The condition x ∈ ℝ, x ≠ 0 means that x may be any real number except zero. The negative real numbers are represented by the open interval (-∞, 0), because zero is not included. The positive real numbers are represented by (0, ∞), again with zero excluded. Combining these two disjoint parts with union gives (-∞, 0) ∪ (0, ∞). Square brackets at zero would incorrectly include zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
