If E = {x : x ∈ ℤ, |x - 2| < 1}, choose the correct option for E.
Answer and explanation
Correct answer: E = {2}
For an absolute-value inequality, |x - 2| < 1 is equivalent to -1 < x - 2 < 1. Adding 2 throughout gives 1 < x < 3. The only integer strictly between 1 and 3 is 2. Therefore the set contains exactly one element: E = {2}. The endpoints 1 and 3 are excluded because the original inequality is strict.
Frequently asked questions
What is the correct answer to this question?
E = {2}
Why is this the correct answer?
For an absolute-value inequality, |x - 2| < 1 is equivalent to -1 < x - 2 < 1. Adding 2 throughout gives 1 < x < 3. The only integer strictly between 1 and 3 is 2. Therefore the set contains exactly one element: E = {2}. The endpoints 1 and 3 are excluded because the original inequality is strict.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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