The set of all positive integers less than 50 forming the equivalence class of 8 for modulo 11 is:
Answer & explanation
Correct answer: option 3
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 $\{8, 19, 30, 41\}$.