$\mathrm{The} \mathrm{relation} \mathrm{R}=\{(\mathrm{a},\mathrm{a}),(\mathrm{b},\mathrm{b}),(\mathrm{c},\mathrm{c}),(\mathrm{a},\mathrm{b}),(\mathrm{b},\mathrm{c}),(\mathrm{a},\mathrm{c})\}$ on the set $A=\left\{a,b,c\right\}$ is 

R = {(a, b), (b, b), (c, c), (a, b), (b, c) (a, c)}
Set A = {a, b, c}
for reflexive R{(a, a), (b, b) (c, c)}
so given relation is reflexive
Symmetric
R = {(a, b) (b, a) (a, c) (c, a) (b, c) (c, b)}
So given relation is not reflexive
Transitive
R = {(a, b), (b, c) (a, c)}
So given relation is transitive.