What is the correct answer for A = {x ∈ Z : x² = 2}?
Answer and explanation
Correct answer: A = ∅
The domain is restricted to integers. Although the equation x² = 2 has real solutions x = √2 and x = -√2, neither solution is an integer. No integer square equals 2: the neighboring integer squares are 1² = 1 and 2² = 4, and the same holds for their negatives. Thus no integer satisfies the defining condition, so A has no elements and A = ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
The domain is restricted to integers. Although the equation x² = 2 has real solutions x = √2 and x = -√2, neither solution is an integer. No integer square equals 2: the neighboring integer squares are 1² = 1 and 2² = 4, and the same holds for their negatives. Thus no integer satisfies the defining condition, so A has no elements and A = ∅.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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