Question

Let R be the equivalence relation on the set Z of integers given by R = {(a, b) : 2 divides a – b}. The equivalence class [0] is

• A. {0, 1, 2, 3, 4, 5,.....}
• B. {0, 2, 4, 6, 8,......}
• C. {0, -2, -4, -6, -8,......}
• D. $\left(0,\pm 2,\pm 4,\pm 6,\pm 8,......\right\}$

Answer 1

The correct option is D $\left(0,\pm 2,\pm 4,\pm 6,\pm 8,......\right\}$

$\mathrm{Equivalence}\mathrm{class}\left(0\right]=\left(x\in Z:xR0\right\}\Rightarrow 2\mathrm{divides}(x-0).\Rightarrow 2\mathrm{divides}x.\Rightarrow x\mathrm{is}a\mathrm{multiple}\mathrm{of}2.\Rightarrow x=0,\pm 2,\pm 4,........$