A relation $$\rho$$ is defined on the set of integers $$Z$$ so that $$\varrho = \{(a,b) \in {Z} \times {Z} \mid |a - b| \leq 5\}.$$ The the relation is​

Correct option is B

​$$\textbf{Given:} \\\rho = \{(a, b) \in \mathbb{Z} \times \mathbb{Z} \mid |a - b| \leq 5 \} \\[8pt]\textbf{Check Reflexive:} \\|a - a| = 0 \leq 5 \Rightarrow (a, a) \in \rho \quad \text{(Always true)} \\[6pt]\Rightarrow \text{ρ is reflexive} \\[8pt]\textbf{Check Symmetric:} \\|a - b| \leq 5 \Rightarrow |b - a| = |a - b| \leq 5 \Rightarrow (b, a) \in \rho \\\Rightarrow \text{ρ is symmetric} \\[8pt]\textbf{Check Transitive:} \\\text{Let } a = 1, b = 5, c = 10 \\|a - b| = 4,\quad |b - c| = 5 \Rightarrow (a, b), (b, c) \in \rho \\|a - c| = 9 \nleq 5 \Rightarrow (a, c) \notin \rho \\\Rightarrow \text{ρ is not transitive} \\[10pt]\boxed{\text{Answer: (B) Reflexive and Symmetric}}$$​​