If R is transitive, is the complement of R transitive? Given a relation R on X,
ID: 3121915 • Letter: I
Question
If R is transitive, is the complement of R transitive? Given a relation R on X, define the complement of R to be R, where aRb iff a, b elementof x and not Equivalently, (aRb) R = {(a, b) elementof X times X: (a, b) NOTElement R}. (The relation R is, as a set, the complement of the set R in the universal set X times X.) For each part that follows, if your answer is "no, " provide a relation on a set and elements to give a counterexample: a) If R is reflexive, is R reflexive? If R is not reflexive, must R be reflexive? c) Repeat part a for symmetric. d) Repeat part a for transitive. e) Repeat part a for antisymmetric.Explanation / Answer
True . Since R is transitive
Which means if (x,y) do not belong to R and (b,c) does not belong to R then (a,c) also does not belong to R
This they allbelong to complemwnt of R and hence it forms a transotive relation