Let the set A 0123 and let Y be a relation defined on A suc

Let the set A = {0,1,2,3} and let Y be a relation defined on A such that Y = {(0,0), (0,1), (0,2), (1,2)} Is Y transitive ?

Yes.

For the relation Y to be transitive we need that:

xRy and yRz then xRz

There is only one case in given relation where:

xRy and yRz ie for (0,1) and (1,2)

ie 0R1 and 1R2 so we must have 0R2 which is true as: (0,2) is in Y

Note that aRb is represented here as: (a,b)