Discrete Math Given the following set 1 2 3 4 what is the re

Discrete Math

Given the following set {1, 2, 3, 4} what is the resulting matrix if the relation is:

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

Solution

Given the following set {1, 2, 3, 4} what is the resulting matrix if the relation is:
{(1, 3), (2, 1), (2, 2), (2, 4), (3, 4), (4, 4)}

Answer:
let say set={1,2,3,4} termed as A.
Let say relation={(1, 3), (2, 1), (2, 2), (2, 4), (3, 4), (4, 4)} termed as R.
Now Resulting matrix concept:
It is the |A|*|A| Matrix M with M(i,j)=1 if(i,j) R
and M(i,j)=0 if (i,j) not belong to R.

Hence here,
|A| = 4 therefore M=0 0 1 0
1 1 0 1
0 0 0 1
                           0 0 0 1
As,(1,3) available in R it means first row and third coloumn of matrix M must be 1.Similarly for the other elements present in the Relation R.

Hence final answer:
                              
           0 0 1 0
1 1 0 1
0 0 0 1
           0 0 0 1      

Please let me know in case of any doubt,Thanks.