The set of all positive integers less than 50 forming the equivalence class of 8 for modulo 11 is: |
{8, 16, 24, 32, 40, 48} {11, 22, 33, 44} {8, 19, 30, 41} {8, 19, 27, 35, 43} |
{8, 19, 30, 41} |
The correct answer is Option (3) - {8, 19, 30, 41} $\text{Equivalence class of } 8 \text{ modulo } 11 \Rightarrow x \equiv 8 \pmod{11}$ $x = 8 + 11k$ $k = 0 \Rightarrow x = 8$ $k = 1 \Rightarrow x = 19$ $k = 2 \Rightarrow x = 30$ $k = 3 \Rightarrow x = 41$ $k = 4 \Rightarrow x = 52 \; (>50 \text{ not allowed})$ The set is $\{8, 19, 30, 41\}$. |