CUET · MATHS · PYQ PAPER 2023
Let \(R\) be a relation on the set of integers given by \((x, y) \in R \Longleftrightarrow|x-y| \leq 1\). Then \(R\) is
(A) Reflexive relation
(B) Symmetric relation
(C) Transitive relation
(D) \(R\) is not a function
(E) Empty relation
Choose the correct answer from the options given below:
- A \(A, B\) and \(E\) only
- B \(A, C\) and \(D\) only
- C \(B, C\) and \(D\) only
- D \(A, B\) and \(D\) only
Answer & Solution
Correct Answer
(D) \(A, B\) and \(D\) only
Step-by-step Solution
Detailed explanation
Reflexive: \(|x-x| = 0 \leq 1\). \(R\) is reflexive. Symmetric: If \(|x-y| \leq 1\), then \(|y-x| = |x-y| \leq 1\). \(R\) is symmetric. Transitive: Let \(x=1, y=2, z=3\). \( (1,2) \in R \) as \( |1-2|=1 \). \( (2,3) \in R \) as \( |2-3|=1 \). But \( (1,3) \notin R \) as…
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