let R be the equivalence relation in the set A= {0,1,2,3,4,5}given by R={(a,b) : 2 divides (a-b)}.write equivalence class {0}.

Hi Nirmitasha,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{A}=\left\{0,1,2,3,4,5\right\} \\ \mathrm{R}=\left(\mathrm{a},\mathrm{b}\right):2 \mathrm{divides} \left(\mathrm{a}-\mathrm{b}\right) \\ \Rightarrow \left(\mathrm{a}-\mathrm{b}\right) \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 2. \\ \mathrm{To} \mathrm{find} \mathrm{equivalence} \mathrm{class} \left\{0\right\}, \mathrm{put} \mathrm{b}=0 \\ \Rightarrow \mathrm{a}-0 \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 2. \\ \Rightarrow \mathrm{a} \mathrm{is} \mathrm{a} \mathrm{multiple} \mathrm{of} 2. \\ \mathrm{Multiples} \mathrm{of} 2 \mathrm{in} \mathrm{given} \mathrm{set} \mathrm{A} \mathrm{are} 0,2 \mathrm{and} 4. \\ \mathbf{Hence}\mathbf{ }\mathbf{ }\mathbf{equivalence}\mathbf{ }\mathbf{class}\mathbf{ }\left\{\mathbf{0}\right\}\mathbf{=}\left\{\mathbf{0}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{4}\right\} \end{gathered}$$

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