Question #308397

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__________.

1
Expert's answer
2022-03-10T02:55:55-0500

Solution


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


We consider a relation on a set AA, let it be RR.


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


We represent it mathematically as,


R=R1R2R3....RnR^{*}=R^{1}\cup R^{2}\cup R^{3}....\cup R^{n}


Therefore, the answer for the given blank space is


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




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