GATE CSE 1989 | Question: 1-iv

Question

The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.

Answer 1

Transitive closure can be found using a directed graph.

Answer 2

The transitive closure of the relation  R = {(1,2),(2,3),(3,4),(5,4)} on the set means if it is transitive then it follows transitive property 

whenever R relates a to b and b to c, then R also relates a to c.

therefore

(1,2), (2,3)       => (1,3)

(2,3), (3,4)      =>(2,4)

(1,2), (2,4)      =>(1,4)

The transitive closure of the relation R = {(1,2),(2,3),(1,3) ,(3,4),(2,4),(1,4),(5,4)}

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hope my answer helps u a lot