Question $3$

Consider the following relation on the set A$=$a$,$b$,$c$,$d :

R$=\{($a$,$a$),($a$,$b$),($b$,$a$),($b$,$c$),($c$,$d$),($d$,$d$)\}.$

Part a: Give the reflexive closure of R$.$ You can represent your answer using a graph, a set of tuples,

or a matrix.

Part b: Give the symmetric closure of R$.$ You can represent your answer using a graph, a set of

tuples, or a matrix.

Part c: Give the transitive closure of R$.$ You can represent your answer using a graph, a set of tuples,

or a matrix.