If A = {x ∈ R : x ≤ 0} and B = {x ∈ R : x ≥ 0}, what is A ∩ B?
Answer and explanation
Correct answer: {0}
A consists of all real numbers less than or equal to zero, while B consists of all real numbers greater than or equal to zero. A number in the intersection must satisfy both x ≤ 0 and x ≥ 0 simultaneously. The only real number satisfying both inequalities is x = 0. Since both inequalities include equality, zero belongs to both sets, so A ∩ B = {0}.
Frequently asked questions
What is the correct answer to this question?
{0}
Why is this the correct answer?
A consists of all real numbers less than or equal to zero, while B consists of all real numbers greater than or equal to zero. A number in the intersection must satisfy both x ≤ 0 and x ≥ 0 simultaneously. The only real number satisfying both inequalities is x = 0. Since both inequalities include equality, zero belongs to both sets, so A ∩ B = {0}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
