Let $X$ = {$a,b,c,d,e$}. Let us call a binary relations $R$ on $X$ special if it satisfies all of the following conditions: (i) $R$ is reflexive, (ii) $R$ is symmetric and (iii) $R$ contains the pair ($a,b$). Find the number of special binary relations on $X$ you need not simplify your answer.
What I want to know is that why the number of reflexive relation is not $1$? As I know only {$(a,a),(b,b),(c,c),(d,d),(e,e)$} is reflexive. So one.. I know it must be wrong. Is there anybody to let me know?
And also I think the relation must contain {{$(a,a),(b,b),(c,c),(d,d),(e,e),(a,b),(b,a)$} I do know know how to solve it from here.