Question

Let R be the equivalence relation on the set Z of the integers given by R = {(a, b) : 2 divides a $-$ b}. Write the equivalence class [0].
[NCERT EXEMPLAR]

Answer 1

We have,
An equivalence relation, R = {(a, b) : 2 divides a $-$ b}

$$\begin{gathered} \mathrm{If}b=0,\mathrm{then}a-b=a-0=a \\ \mathrm{As},2\mathrm{divides}\mathrm{a}-\mathrm{b} \\ \mathrm{And},\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{integers}\mathrm{which}\mathrm{are}\mathrm{divided}\mathrm{by}2\mathrm{is}\left\{0,\pm 2,\pm 4,\pm 6,...\right\} \\ \mathrm{So},\mathrm{the}\mathrm{equivalence}\mathrm{class}\left[0\right]=\left\{0,\pm 2,\pm 4,\pm 6,...\right\} \end{gathered}$$