Question

The set of all positive integers less than 50 forming the equivalence class of 8 for modulo 11 is:

• A. {8, 16, 24, 32, 40, 48}
• B. {11, 22, 33, 44}
• C. {8, 19, 30, 41}
• D. {8, 19, 27, 35, 43}

Answer 1

The Correct Option is C

To find the set of all positive integers less than 50 forming the equivalence class of 8 for modulo 11, we need to determine the integers \( x \) such that:

\[ x \equiv 8 \ (\text{mod} \ 11) \]

This means that when \( x \) is divided by 11, the remainder is 8. We start at 8 and keep adding 11 until we reach 50:

• 8
• 8 + 11 = 19
• 19 + 11 = 30
• 30 + 11 = 41

41 + 11 = 52, which is greater than 50, so we stop here. Therefore, the set of integers less than 50 that form the equivalence class of 8 mod 11 is \({8, 19, 30, 41}\).