If Q₁ = {x : x ∈ ℤ, 2x + 1 = 0}, what is Q₁?
Answer and explanation
Correct answer: Q₁ = ∅
Solving the equation 2x + 1 = 0 gives 2x = −1 and hence x = −1/2. Although this is a solution over the real or rational numbers, it is not an integer. The definition of Q₁ specifically restricts x to ℤ, the set of integers. Therefore no integer satisfies the condition, and Q₁ contains no elements. Hence Q₁ is the empty set, written as ∅.
Frequently asked questions
What is the correct answer to this question?
Q₁ = ∅
Why is this the correct answer?
Solving the equation 2x + 1 = 0 gives 2x = −1 and hence x = −1/2. Although this is a solution over the real or rational numbers, it is not an integer. The definition of Q₁ specifically restricts x to ℤ, the set of integers. Therefore no integer satisfies the condition, and Q₁ contains no elements. Hence Q₁ is the empty set, written as ∅.
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.
