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## Homework Statement

~ is a equivalence relation on integers defined as:

a~b if and only if 2a+3b is divisible by 5

What is the equivalence class of 0

## Homework Equations

## The Attempt at a Solution

[0] = {0, 5n} n is an integer

My reasoning for choosing 0 is that if a=0 and b=0, the relation is satisfied since 2(0)+3(0) = 0 and 5 divides 0, so 0~0

My reasoning for choosing 5n is that if a=0 and b=5n, or the other way around, then 2(0)+3(5n)=3(5n), which is a multiple of 5, and thus divisible by 5, satisfying the relation, making 0~5n

I got 0 marks for the question, but I don't know if it's because the statement isn't assembled properly, or if it's because I don't know what an equivalence class is. Please help me see my error