Solution:

Given set A = {x ∈ Z; 0 ≤ x ≤ 12}

Also given that relation R = {(a, b): a = b} is defined on set A

Now we have to check whether the given relation is equivalence or not.

To prove equivalence relation it is necessary that the given relation should be reflexive, symmetric and transitive.

Reflexivity:

Let a be an arbitrary element of A.

Then, a ∈ R

⇒ a = a          [Since, every element is equal to itself]

⇒ (a, a) ∈ R for all a ∈ A

So, R is reflexive on A.

Symmetry:

Let (a, b) ∈ R

⇒ a b

⇒ b = a

⇒ (b, a) ∈ R for all a, b ∈ A

So, R is symmetric on A.

Transitivity:

Let (a, b) and (b, c) ∈ R

⇒ a =b and b = c

⇒ a = b c

⇒ a = c

⇒ (a, c) ∈ R

So, R is transitive on A.

Hence, R is an equivalence relation on A.

Therefore R is reflexive, symmetric and transitive.

The set of all elements related to 1 is {1}.