Question

Use Warshall's algorithm to find the transitive closures of the relation R = {(1,2). (2.1). (2,3). (3,4), (4,1)) for the set A = {1,2,3,4} ​

Answer 1

Answer:

YEAP..!!

Explanation:

Define Reflexive closure, Symmetric closure along with a suitable example. Let R be a relation on

Set S= {a, b, c, d, e), given as

R = {(a, a),(a, d), (b, b) , (c, d) , (c, e) , (d, a), (e, b), (e, e)}

Find transitive closure using Warshall's Algorithm.

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Answer 2

Answer:

W4=                 Required transitive closure

1   1   1   1

1   1   1   1

1   1   1   1

1   1   1   1

Explanation:

W0 =                            

0   1   0   0

1    0   1   0

0   0   0   1

1    0   0   0

 

W1 =

0   1   0   0

1    1    1   0

0   0   0   1

1     1   0   0

W2=

1   1   1   0

1   1   1   0

0  0  0   1

1    1   1   0

W3=

1   1   1   1

1   1   1   1

0  0  0  1

1   1   1   1

W4=                 Required transitive closure

1   1   1   1

1   1   1   1

1   1   1   1

1   1   1   1