If L₁ = {x : x ∈ ℤ, |x| = -2}, what is L₁?
Answer and explanation
Correct answer: Empty set
The absolute value of every real number, and therefore of every integer, is always non-negative. It can be zero or positive, but it can never equal -2. Thus there is no integer x satisfying |x| = -2. A set defined by a condition with no possible solution contains no elements, so L₁ is the empty set, denoted by ∅.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
The absolute value of every real number, and therefore of every integer, is always non-negative. It can be zero or positive, but it can never equal -2. Thus there is no integer x satisfying |x| = -2. A set defined by a condition with no possible solution contains no elements, so L₁ is the empty set, denoted by ∅.
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.
