Let R be a relation on the open interval (-1,1) and is given by R=\{(x,y):|x+y| \lt 2\}. Then which one of the following is correct?
- A. R is reflexive but neither symmetric nor transitive
- B. R is reflexive and symmetric but not transitive
- C. R is reflexive and transitive but not symmetric
- D. R is an equivalence relation ✓
Correct Answer: D. R is an equivalence relation
Explanation
For any x, y \in (-1, 1), their sum x+y always satisfies -2 \lt x+y \lt 2, which means |x+y| \lt 2. Thus, the relation R relates every pair in the interval (-1, 1). This forms a universal relation, which is always an equivalence relation.
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