Answer is D.
A binary relation $R$ over a set $X$ is symmetric if it holds for all $a$ and $b$ in $X$ that if $a$ is related to $a.$
$\forall_{a,b} \in X,aRb \Rightarrow bRa.$
Here $(x,y)$ is there in $R$ but $(y,x)$ is not there.
$\therefore$ Not Symmetric.
For Antisymmetric Relations: $\forall_{a,b} \in X, R(a,b) \;\& \;R(b,a)\Rightarrow a=b.$
Here $(x,z)$ is there in $R$ also $(z,x)$ is there violating the antisymmetric rule.
$\therefore$ Not AntiSymmetric.