Question: (10 points) Given a directed graph G=(V,E), define the relation R on V, where xRy if there exists a path from x to y, or

(10 points) Given a directed graph G=(V,E), define the relation R on V, where xRy if there exists a path from x to y, or if x=y, for some x,y V.

(a) Disprove that R is an equivalence relation.

(b) Make a change to the definition of R to make it an equivalence relation.

(c) Prove your modified R is an equivalence relation and

(d) Specify the equivalence classes.

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