Answer to Question #128925 in Discrete Mathematics for usama

Question #128925
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 = \\begin{bmatrix}\n 1 & 0 & 0 &0 \\\\\n 0 & 1 & 0 & 0\\\\ 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0& 1\\\\\n\\end{bmatrix}" .

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 "A_{ii} = 1 \\ forall \\ i = 1,2,3,4" .

Symmetric since "A_{ij} = A_{ji}" for all "i,j = 1,2,3,4"

and Anti-symmetric since "A_{ij} = A_{ji}" for all "i,j = 1,2,3,4"

d) Given matrix is transitive also since "A_{ii} = 1 , A_{ij} = 0 \\ if \\ i \\neq j" .

Hence the relation for this graph is equivalence.



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Comments

Assignment Expert
09.08.20, 22:39

Dear ali, please use the panel for submitting new questions.

ali
08.08.20, 08:22

Find the floor and ceiling Function of x and . Take any value of x and y. (5) X Floor Ceiling -X.Y (x point y) X / Y (x divided by y)

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