Answer
a. See graph
b. Not Reflexive
c. Not Symmetric
d. Not Transitive
Work Step by Step
a. See graph
b. Reflexive:
A relation $𝑅$ is reflexive if for every element
$𝑎$ in the set, $(a,a)\in R$.
The elements appearing in the relation are 0, 1, 2, and 3.
For reflexivity, we need (0,0), (1,1), (2,2), and (3,3) to be present.
Checking the relation:
$(2,2)$ is missing
Since $(2,2)$ is missing, the relation is not reflexive.
c. Symmetric:
A relation $R$ is symmetric if whenever $(a,b)\in R$, then $(b,a)\in R$ also.
Checking pairs:
$(0,3)$ is in R, but $(3,0)$ is missing.
Since $(0,3)$ does not have the symmetric pair, the relation is not symmetric.
d. Transitive:
A relation $R$ is transitive if whenever $(a,b)\in R$ and $(b,c)\in R$, we have $(a,c)\in R$.
Checking pairs:
$(1,0)$ and $(0,3)$ exist, but $(1,3)$ is missing.
Since $(1,3)$ is missing, the relation is not transitive.
