Question

Let be the congruence relation modulo 7 on . then the equivalence class [110] equals to which of the following?

a. [3]
b. [2]
c. [4]
d. [5]
e. [1]

Answer 1

The equivalence class [110] modulo 7 is equal to [5], as both 110 and 5 have the same remainder when divided by 7.

Step-by-step explanation:

The student has asked about the equivalence class of the number 110 modulo 7. To find the equivalence class, we calculate 110 modulo 7, which is the remainder of 110 divided by 7. So, we calculate 110 ÷ 7, which equals 15 remainder 5. Thus, 110 is congruent to 5 modulo 7.

This means that 110 belongs to the same set of numbers that, when divided by 7, also have a remainder of 5. In other words, the equivalence class [110] is equal to the equivalence class [5] because both numbers have the same remainder when divided by 7. Therefore, the correct answer is option d. [5].