Answer to Question #282059 in Discrete Mathematics for feey

Question

LetR={(1,2),(2,1),(2,3),(2,4),(4,1),(4,3)}

R={(1,2),(2,1),(2,3),(2,4),(4,1),(4,3)}

is a relation on

setA={1,2,3,4}

Suppose   aRnb

means that there is a path of length n

from a to b

Which of elements are of

R∞

Answer 1

Question: Let R={(1,2),(2,1),(2,3),(2,4),(4,1),(4,3)} is a relation on setA={1,2,3,4}. Suppose aRnb

means that there is a path of length n from a to b. Which of the elements are of Reflexive & symmetric?

Solution:

R={(1,2),(2,1),(2,3),(2,4),(4,1),(4,3)}

Reflexive elements: When (a,a)$\in$R, $\forall a\in$R

So, no reflexive elements.

Symmetric elements: When (a,b)$\in$R, then (b,a)$\in$R

So, (1,2), (2,1) are symmetric elements.