$\bullet$ Question A is:
We are given $R = \{(1, 1), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (3, 4), (4, 1), (4, 4)\}$.
It is reflexive because $(1,1)$, $(2,2)$, $(3,3)$, $(4,4)$ is in the set.
It is antisymmetric because $(b,a)$ is not in the set for any of the pairs.
It is not transitive because $(1,1)$ is missing from the set.
Is this correct?
$\bullet$ Question B is:
Given the relation $S = \{(1, 2), (2, 3), (2, 4), (4, 2)\}$.
Name the transitive closure $\hat{S}$ of $S$.
So we must also have $(2,1)\in\hat{S}$ and $(1,3)\in\hat{S}$.
$\bullet$ Remark:
$R$ is said to be transitive, if:
$(a, b) \in R$ and $(b, a) \in R \Rightarrow (a, c) \in R$,