The given code starts by initializing some sets and relations f$,$ g$,$ h$,$ and r$.$Block $3$ tests if the relation g on D$1$ is symmetric. Run the code and observe the output.In Block $4$ write a test to determine if relation h on D$2$ is anti$-$symmetric. Your code should output any pairs showing that h is not anti$-$reflexive on D$2.$In Block $5$ write a test to determine if relation f on D$1$ is transitive. Your code should output any triples showing that f is not transitive on D$1.$In Block $6$ write a test to determine if relation r on D$1$ is transitive. Your code should output any triples showing that r is not transitive on D$1.$

main.py

# Block $3$: Tests whether relation g on domain D$1$ is symmetric

# Run the code and observe the output. You do not need to add any code in Block $3$

# Assume that g on domain D$1$ is symmetric until proven otherwise

gIsSymmetric $=$ True

for x in D$1$:

for y in D$1$:

if $($x $<=$ y$)$: # We only need to check each pair once, so we will check only when x $<=$ y

if $(($g$($x$,$y$)==$True and g$($y$,$x$)==$False$)$ or $($g$($x$,$y$)==$False and g$($y$,$x$)==$True$))$:

gIsSymmetric $=$ False # An x$,$ y in the domain is found where g$($x$,$y$)$ and g$($y$,$x$)$ are not the same

# The flag gIsAntiReflexive can never be set back to true.

print$(\text{'}$The pair $(\text{'}+$ str$($x$)+\text{'},\text{'}+$ str$($y$)+\text{'})$ shows that g is not symmetric'$)$

if $($gIsSymmetric$)$:

print$(\text{'}$The relation g on domain D$1$ is symmetric.$\text{'})$

else:

print$(\text{'}$The relation g on domain D$1$ is not symmetric.$\text{'})$

print$(\text{'}\text{'})$

# Block $4$: Tests whether relation h on domain D$2$ is anti$-$symmetric

# Assume that h on domain D$2$ is symmetric until proven otherwise

# Use the following line if a pair is reached showing that h is not anit$-$symmetric on domain D$2$:

# print$(\text{'}$The pair $(\text{'}+$ str$($x$)+\text{'},\text{'}+$ str$($y$)+\text{'})$ shows that h is not anti$-$symmetric'$)$

hIsAntiSymmetric $=$ True

# Put your code here to test if h on domain D$2$ is anti$-$symmetric

if $($hIsAntiSymmetric$)$:

print$(\text{'}$The relation h on domain D$2$ is anti$-$symmetric.$\text{'})$

else:

print$(\text{'}$The relation h on domain D$2$ is not anti$-$symmetric.$\text{'})$

print$(\text{'}\text{'})$

# Block $5$: Tests whether relation f on domain D$1$ is transitive

# Assume that f on domain D$1$ is transitive until proven otherwise

# Note that each triple $($x$,$y$,$z$)$ must be tested in every possible order

# Use the following line if a triple is reached showing that f is not transitive on domain D$1$:

# print$(\text{'}$The triple $(\text{'}+$ str$($x$)+\text{'},\text{'}+$ str$($y$)+\text{'},\text{'}+$ str$($z$)+\text{'})$ shows that f is not transitive'$)$

fIsTransitive $=$ True

# Put your code here to test if f on domain D$1$ is transitive

if $($fIsTransitive$)$:

print$(\text{'}$The relation f on domain D$1$ is transitive.$\text{'})$

else:

print$(\text{'}$The relation f on domain D$1$ is not transitive.$\text{'})$

print$(\text{'}\text{'})$

# Block $6$: Tests whether relation r on domain D$1$ is transitive

# Assume that r on domain D$1$ is transitive until proven otherwise

# Note that each triple $($x$,$y$,$z$)$ must be tested in every possible order

# Use the following line if a triple is reached showing that r is not transitive on domain D$1$:

# print$(\text{'}$The triple $(\text{'}+$ str$($x$)+\text{'},\text{'}+$ str$($y$)+\text{'},\text{'}+$ str$($z$)+\text{'})$ shows that r is not transitive'$)$

rIsTransitive $=$ True

# Put your code here to test if r on domain D$1$ is transitive

if $($rIsTransitive$)$:

print$(\text{'}$The relation r on domain D$1$ is transitive.$\text{'})$

else:

print$(\text{'}$The relation r on domain D$1$ is not transitive.$\text{'})$

print$(\text{'}\text{'})$