If Q = {x : x ∈ N, x² < 0}, what is Q?
Answer and explanation
Correct answer: Q = ∅
The square of every natural number is non-negative: for every x ∈ N, x² ≥ 0. Hence the inequality x² < 0 cannot be satisfied by any natural number. There is therefore no element that belongs to Q. By definition, a set with no elements is the empty set, so Q = ∅. The choices Q = N, {0}, or {1} are impossible because each would contain elements whose squares are not negative.
Frequently asked questions
What is the correct answer to this question?
Q = ∅
Why is this the correct answer?
The square of every natural number is non-negative: for every x ∈ N, x² ≥ 0. Hence the inequality x² < 0 cannot be satisfied by any natural number. There is therefore no element that belongs to Q. By definition, a set with no elements is the empty set, so Q = ∅. The choices Q = N, {0}, or {1} are impossible because each would contain elements whose squares are not negative.
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.
