Discrete Equivalence Relation reflexive,symmetric, anti-symmetric, transitive

Question

The binary relation $R$ on $X = \{a, b, c, d\} $ is given by $R = \{(a, a), (a, b), (b, b), (c, c), (c, d), (d, c)\}$.

Determine if $R$ is reflexive, symmetric, anti-symmetric and / or transitive.

My solution is that I thought it was symmetric because of $cRd \Longrightarrow dRc.$

It is wrong. In the answer they say it is none of reflexive,symmetric, anti-symmetric, and / or-transitive??

Answer 1

1. For $(a,b)$ it is symmetric but you must show it for all pairs of $R$ that it is symmetric.Is it symmetric for all pairs of $R$?
2. For $a\in X$ it is reflexive because $(a,a) \in R$. But you must show for all elements $x\in X$ that $(x,x) \}\in R$. Is this true for all $x$ in $X$?
3. ...