Consider a (binary) relationRon a non-empty setSconsisting of points in a plane.

Consider a (binary) relationRon a non-empty setSconsisting of points in a plane. Letaandbbe two
elements ofS i.e.ab?S and defineRsuch thata R biff there is a directed path fromatob.
Consider the setS={abc}with(ab)(bc)(cd)?R1. IsR1transitive? Show this.
Consider the setS={abc}with(ab)(bc)(cb)(cd)(ac)(bd)?R2. IsR2transitive? Show
this.
Define the transitive closure ofRtofR.
Construct the transitive closure ofR1.
Provide a concise description of the method (algorithm) you used to construct the transitive closure
ofR1.
Givennpoints in the plane what is the maximum number of distinct directed paths that can connect
these points. (This problem requires you to carefully define the structure of the points in the plane).