Q4 Write down any 4*4 matrix having only zeros and ones. (3*5=15)
a) Draw the Directed graph of that matrix.
b) List the ordered pairs in the relation on set {1, 2, 3, 4} corresponding to this matrix.
c) Determine whether the relations on this graph/ matrix are Reflexive, Symmetric and Anti-symmetric.
d) Determine whether the relation for this graph is equivalence or not?
1
Expert's answer
2020-08-13T18:42:52-0400
Let the matrix is A=⎣⎡1000010000100001⎦⎤ .
a) Directed graph is as follows:
b) Ordered pairs in the relation on set {1, 2, 3, 4} corresponding to this matrix = {(1,1),(2,2),(3,3),(4,4)}
c) Given matrix is Reflexive since Aii=1foralli=1,2,3,4 .
Symmetric since Aij=Aji for all i,j=1,2,3,4
and Anti-symmetric since Aij=Aji for all i,j=1,2,3,4
d) Given matrix is transitive also since Aii=1,Aij=0ifi=j .
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