Recall that,

R is symmetric if for all x, y ∈ A, if xRy, then yRx.

R is transitive if for all x, y, z ∈ A, if xRy and yRz, then xRz.

We have relation R = {(a, a), (b, c), (a, b)} on A.

A = {a, b, c}

For Transitive:

If (a, b) ∈ R and (b, c) ∈ R

Then, (a, c) ∈ R

∀ a, b, c ∈ A

For Reflexive:

∀ a, b, c ∈ R

Then, (a, a) ∈ R

(b, b) ∈ R

(c, c) ∈ R

We need to add (b, b), (c, c) and (a, c) in R.

We get

R = {(a, a), (b, b), (c, c), (a, b), (b, c), (a, c)}