If A = {x ∈ R : x is both rational and irrational}, what will A be?
Answer and explanation
Correct answer: A = ∅
Every real number is either rational or irrational, but no real number can be both. A rational number can be written as p/q, where p and q are integers and q ≠ 0; an irrational number cannot be represented in that form. These two categories are disjoint, so the condition requiring both properties has no solution. Hence A is the empty set ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
Every real number is either rational or irrational, but no real number can be both. A rational number can be written as p/q, where p and q are integers and q ≠ 0; an irrational number cannot be represented in that form. These two categories are disjoint, so the condition requiring both properties has no solution. Hence A is the empty 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.
