1.

The transitive closure of the relation {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)}on the set {1, 2, 3, 4, 5}is _______(a) {(0,1), (1,2), (2,2), (3,4)}(b) {(0,0), (1,1), (2,2), (3,3), (4,4), (5,5)}(c) {(0,1), (1,1), (2,2), (5,3), (5,4)}(d) {(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)}This question was addressed to me in exam.My doubt is from Closure on Relations topic in division Relations of Discrete Mathematics

Answer»

Correct choice is (d) {(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)}

Easiest explanation: Let R be a relation on a set A. The CONNECTIVITY relation on R* consists of PAIRS (a,b) such that there is a path of length at LEAST ONE from a to b in R. Mathematically, R* = R^1∪ R^2∪ R^3 ∪ … ∪ R^n. Hence the ANSWER is {(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)}.



Discussion

No Comment Found

Related InterviewSolutions