CUET · MATHS · PYQ PAPER 2025
Assume that R is a relation on the set \(\mathbb{Z}\) of integers and it is given by \((x, y) \in R \Leftrightarrow|x-y| \leq 1\). Then, \(R\) is
- A Reflexive and symmetric but not transitive
- B An equivalence relation
- C Symmetric and transitive but not reflexive
- D Reflexive and transitive but not symmetric
Answer & Solution
Correct Answer
(A) Reflexive and symmetric but not transitive
Step-by-step Solution
Detailed explanation
Reflexive: For any \(x \in \mathbb{Z}\), \(|x-x| = |0| = 0 \leq 1\). Thus, \((x,x) \in R\). R is reflexive. Symmetric: If \((x,y) \in R\), then \(|x-y| \leq 1\). Since \(|y-x| = |-(x-y)| = |x-y|\), it implies \(|y-x| \leq 1\). Thus, \((y,x) \in R\). R is symmetric. Transitive:…
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