in Set Theory & Algebra
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21 votes
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 ___________.
in Set Theory & Algebra
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6 Answers

26 votes
26 votes
Best answer

Transitive closure of $R$

  1. It is transitive.
  2. It contains $R.$
  3. It is minimal satisfies $1$ and $2.$

$R =  {(1,2),(2,3),(3,4),(5,4)}$

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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4 Comments

Is this an standard defination, i didnt find it anywhere can you provide me some reference to it.
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1
is (1,4) necessary?

aRb and bRc implies aRc

so (1,2) , (2,3) => (1,3)

(2,3), (3,4) =>(2,4)

 

why (1,4)?
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0
edited by
$(1, 2), (2, 4) => (1, 4)$
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2

(1,3),(3,4) → (1,4)

(1,2),(2,4) → (1,4)

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4
33 votes
33 votes

Ans{(1,2),(2,3),(1,3) ,(3,4),(2,4),(1,4),(5,4)}

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3 Comments

Best Solution
1
1
@mohan123 Thanks bro.
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This is the best way to answer such questions
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0
24 votes
24 votes
draw a directed graph

Transitive closure can be found using the graph.Include all the pair of vertices for which the path exist in the graph
by

2 Comments

perfect!
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0
Good aproach
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0
15 votes
15 votes

The transitive closure of the relation $\left \{ (1,2),(2,3),(3,4),(5,4)\right \}$ =$\left \{ (1,2),(2,3),(1,3) ,(3,4),(2,4),(1,4),(5,4)\right \}$

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