Given a set $A=\{x \in Z:0 \leq x\leq 12\}$ and relation $R=\{(a,b):a=b)\}$:

Let $a=b$. For every $a \in A (a,a) \in R$, $a=a$. Therefore R is reflexive.

If $(a,b) \in R$ then $a=b$. Similarly, if $(b,a) \in R$, then $b=a$. Therefore, R is symmetric.

If $(a,b) \in R$ then $a=b$ and, if $(b,c) \in R$, then $b=c$.

Now, if $(a,c) \in R$ then $a=c$. Since $a=b$ and $b=c$ $\rightarrow$ $a=c$. Therefore, R is transitive..

Hence $R$ is an equivalence relation as its reflexive, symmetric and transitive.

Given a set $A=\{x \in Z:0 \leq x\leq 12\}$, the set of elements in $A$ is $\{0,1,2,3,4,5,6,7,8,9,10,11,12\}$

Among these elements the ones that are related to 1 are those that satisfy the condition $a=1$.

We can observe that only element that satisfies this condition is $\{1\}$.