Answer to Question #308397 in Discrete Mathematics for Mayur

Question

The number of transitive closure exists in the relation R = {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} where {1, 2, 3, 4, 5} ∈ A is__________.

Answer 1

Solution

Given that $R = \left \{ (0,1), (1,2), (2,2), (3,4), (5,3), (5,4) \right \}$

We consider a relation on a set $A$, let it be $R$.

Then the connectivity relation on $R^{*}$ will consist of the pairs of the form $(a, b)$ , with this condition that there is the path length of at least one $(=1)$ from $a$ to $b$.

We represent it mathematically as,

$R^{*}=R^{1}\cup R^{2}\cup R^{3}....\cup R^{n}$

Therefore, the answer for the given blank space is

$R = \left \{ 1, 2, 3, 4, 5 \right \}∈ A$ is $\left \{ (0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4) \right \}$