Question

The transitive closure of the relation {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} on the set {0,1, 2, 3, 4, 5} is ___

Answer 1

Answer:

The answer of this question is 1

Answer 2

The transitive closure of the relation {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} on the set {0,1, 2, 3, 4, 5} is  {(0,1),(0,2),(1,2),(2,2),(3,4),(5,3),(5,4)}

Explanation:

Given: The transitive closure of the relation {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} on set {0,1, 2, 3, 4, 5}

Transitive closure

• The smallest relation on X that contains R and is transitive is the transitive closure of a binary relation R on a set X.
• In terms of finite sets, the term "smallest" can be interpreted as meaning that there are the fewest related pairs; in terms of infinite sets, it refers to the only minimal transitive superset of R.

R = {(0,1),(1,2),(2,2),(3,4),(5,3),(5,4)}

Let us consider a relation on a set A then let it be R

Then the connectivity relation R* will consist of the pairs of the forms(a,b)

By this condition that there is the path length of at least one from a to b in R

Then we can represent it mathematically as,

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

Therefore the transitive closure is {(0,1),(0,2),(1,2),(2,2),(3,4),(5,3),(5,4)}

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

Final answer:

The transitive closure of the relation {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} on the set {0,1, 2, 3, 4, 5} is  {(0,1),(0,2),(1,2),(2,2),(3,4),(5,3),(5,4)}

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