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An Equivalence relation R on Z defined by aRb if 5a=2b(mod3). which of the following is an equivalence class of R?
1. The Set {x ∈ Z: x=3y for some y∈Z}
2. The even integers
3. The odd integers
4. the set {x: x ∈ Z}

$aRb = { (a,b): 5a\equiv 2b (mod3) }$

1. Set containing all elements containing at least 1 3s as multiple.

From relation, $5a - 2b \equiv 0(mod 3)$

$\Rightarrow 5a - 2b = 3k$ for some k.

Since a & b are multiple of 3. For all a & b We can have,

$\Rightarrow 3(5a' - 2b') = 3k$

Which means for every a & b. Given relation is being satisfied therefore a & b in the class.

2. Counter example S = { 2,4 }

3. Counter example S = { 1,3}

4. Counter example S = { 2,4}

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