Let `R` be the equivalence relation in the set `A={0,\ 1,\ 2,\ 3,\ 4,\ 5}` given by `R={(a ,\ b):2` divides `(a-b)}` . Write the equivalence class [0].

Explanation

To find the equivalence class \([0]\) under the equivalence relation \(R\) defined on the set \(A = \{0, 1, 2, 3, 4, 5\}\) by \(R = \{(a, b) : 2 \text{ divides } (a - b)\}\), we need to determine which elements of \(A\) are related to \(0\) according to the relation \(R\).

### Step-by-Step Solution:

1. **Understanding the Relation**: The relation \(R\) states that \(a\) is related to \(b\) if \(2\) divides \(a - b\). This means that the difference \(a - b\) must be an even number.

2. **Finding the Equivalence Class**: The equivalence class \([0]\) consists of all elements \(a \in A\) such that \(2\) divides \(a - 0\). This simplifies to checking which elements \(a\) in \(A\) are even, since \(a - 0 = a\).

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