Let = {x ∈ Z ∶ 0 ≤ X ≤ 12} and relation R on set A is defined as 

R = {(a, b): |a − b|is a multiple of 4}.

Reflexivity : Let a ∈ A. 

Now, |a − b| = 0 which is a multiple of 4. 

Therefore, (a, a) ∊ R ∀ a ∈ A. 

Hence, the relation R is reflexive relation on set A.

Symmetricity : Let a, b ∈ A such that (a, b) ∊ R.

⇒ |a − b| is a multiple of 4. 

⇒ |b − a| is a multiple of 4. ( \(\because\) |a − b| = |−(b − a)| = |b − a|) 

⇒ (b, a) ∊ R ∀ a, b ∈ A. 

Hence, if (a, b) ∊ R. 

Then, (b, a) ∊ R ∀ a, b ∈ A. 

Thus, the relation R is symmetric relation on set A.

Transitivity : Let a,b,c ∈ A such that (a,b) ∊ R and (b,c) ∊ R. 

⇒ |a - b| is a multiple of 4 and |b - c| is a multiple of 4. 

⇒ a - b = 4m₁ and b - c = 4m₂, where m₁ and m₂ ∊ Z. 

⇒ a - c = a - b + b - c = 4m₁ − 4m₂ = 4(m₁ − m₂ ) = 4m, where m = m₁ − m₂ ∈ Z. 

⇒ |a - c| is a multiple of 4. 

⇒ (a, c) ∊ R ∀ a,b,c ∈ A.

Hence, if (a, b) ∊ R and (b, c) ∊ R. Then, (a, c) ∊ R ∀ a,b,c ∈ A. 

Thus, the relation R is transitive relation on set A. 

Let b ∈ A is image of 1 under the relation R. 

Therefore, |1 − b| is a multiple of 4 and b ∈ A. 

⇒ 1 − b = 4n, where n ∊ z, 0 ≤ b ≤ 12 and b ∈ z.

⇒ b = 1 − 4n, where 0 ≤ b ≤ 12 and b, n ∈ Z. ( b lies in the range [0, 12] is possible only when n have values 0, −1, −2. ) 

⇒ b ∈ {1, 5, 9}.

Hence, the set of elements related to 1 is {1,5,9}.