Question

let R={(1,2),(2,2),(2,3)) be a relation on the set {1,2,3}, find R+
and R*

Answer 1

$\bf R^* = \{ \epsilon, (1,2),(2,2),(2,3), [{(1,2),(2,2)],[{(1,2)(2,3)],[{(2,2),(2,3)],[{((2,3),(2,2)]....... \}$ and$\bf R^+ = \{ (1,2),(2,2),(2,3), [{(1,2),(2,2)],[{(1,2)(2,3)],[{(2,2),(2,3)],[{((2,3),(2,2)]....... \}$

Given:

R={(1,2),(2,2),(2,3)} is a relation on the set {1,2,3}

To Find:

$R^*\\R^+$

Solution:

For a set {"a", "b", "c"}, the Kleene star is applied as

$[ "a", "b", "c" ]^*$$= [ \epsilon, "a", "b", "c", "aa", "ab", "ac", "ba", "bb", "bc", "ca", "cb", "cc", "aaa", "aab", ..].$

Hence If R = {(1,2),(2,2),(2,3)} , and the Kleene star is applied to this set, then

$R^* = \{ \epsilon, (1,2),(2,2),(2,3), [{(1,2),(2,2)],[{(1,2)(2,3)],[{(2,2),(2,3)],[{((2,3),(2,2)]....... \}$

For a set {"a", "b", "c"}, the Kleene plus is applied as

$[ "a", "b", "c" ]^+$ $= [ "a", "b", "c", "aa", "ab", "ac", "ba", "bb", "bc", "ca", "cb", "cc", "aaa", "aab", ..].$

If R = {(1,2),(2,2),(2,3)} , and the Kleene plus is applied to this set, then

$R^+ = \{ (1,2),(2,2),(2,3), [{(1,2),(2,2)],[{(1,2)(2,3)],[{(2,2),(2,3)],[{((2,3),(2,2)]....... \}$

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