In the first part of the assignment, write a program $($in java$)$ that will determine whether a given $($do$,$n$\text{'}$t u$,$se c$,$hat,g$,$pt$)$

relation is reflexive, symmetric, anti symmetric, transitive, equivalence, and partial order.

The input to the program is a file containing the relation. The input file contains the

binary matrix representing the relation. The $0\text{'}$s and $1\text{'}$s of the matrix are separated by

white spaces. The file also contains the size of the matrix at the top. The output of the

program is a file containing the six decisions about the relation. The program asks the

user for file names.

Run your program with the given relations. Submit the results.

$1.$ask input and output file names

$2.$open input and output files

$3.$ n $=$ read size of matrix

$4.$ x $=$ create array of size nxn

$5.$ read nxn values into x

$6.$ decide whether x is reflexive $[$check $($i$,$i$)$ is $1]$

$7.$ decide whether x is symmetric $[$check $($i$,$j$)$ equals $($j$,$i$)]$

$8.$ decide whether x is antisymmtric $[$check $($i$,$j$)$ and $($j$,$i$)$ are not $1]$

$9.$ decide whether x is transitive $[$find x$^2,$ check x$^2$ is subset of x$]$

$10.$ decide whether x is equivalence $[$check x is reflexive, symmetric, transitive$]$

$11.$ decide whether x is partial order $[$check x is reflexive, antisymmetric, transitive$]$

$12.$ print yes$/$no for six questions