Python 3
Discrete Mathematics
We are going to write a program to read in relations, show the matrix of the relation. We will also show if the relation is reflexive, symmetric, anti-symmetric and transitive. This program will read in files that the user gives. Normal Error handling applies. The file the user gives you will have the elements of the set for the relation followed by the tuples in the relation.
The Text Files
The first line of the text file is all the elements in the set separated by commas. Each line thereafter should contain 2 of the elements separated by a comma.
x,y, z
x,x
y,y
z,z
x, y
Line 1 above is x, y, z. The relation is a binary relation and will be over elements x, y and z. Line 2-5 is a tuple in the relation showing the relationships { (x, x), (y, y), (z, z), (x, y) }
The lines after line 1 should only have 2 elements separated by a single comma. If it doesn’t, then it is an invalid line. Any of the elements in line 2 onward will be an element contained in the first line.
Sample Output
>>> ================================ RESTART ================================
>>> >>> ================================ RESTART ================================
>>> Enter the name of the relation file. Enter quit to exit ==> 1.txt
Relation on set {a,b}
Matrix of Relation
a b
a 0 1
b 1 0
Square of Relation
a b
a 1 0
b 0 1
The relation is not reflexive
The relation is symmetric
The relation is not anti-symmetric
The relation is not transitive
Enter the name of the relation file.
Enter quit to exit ==> nofile.txt
Could not open the file given. Please enter another file
Enter the name of the relation file. Enter quit to exit ==> 2.txt
Relation on set {x,y,z}
Matrix of Relation
x y z
x 1 0 0
y 0 1 0
z 0 0 1
Square of Relation
x y z
x 1 0 0
y 0 1 0
z 0 0 1
The relation is reflexive
The relation is symmetric
The relation is anti-symmetric
The relation is transitive
Enter the name of the relation file. Enter quit to exit ==> 3.txt
Relation on set {a,b,c,d,e}
Matrix of Relation
a b c d e
a 1 1 1 0 0
b 0 1 1 0 0
c 0 0 1 0 0
d 0 0 0 1 1
e 0 0 0 0 1
Square of Relation
a b c d e
a 1 2 3 0 0
b 0 1 2 0 0
c 0 0 1 0 0
d 0 0 0 1 2
e 0 0 0 0 1
The relation is reflexive
The relation is not symmetric
The relation is anti-symmetric
The relation is not transitive
Enter the name of the relation file. Enter quit to exit ==> 4.txt
Relation on set {s,t,u,v,w}
Matrix of Relation
s t u v w
s1 1 0 0 0
t 1 1 0 0 0
u 0 0 1 1 1
v 0 0 1 1 1
w 0 0 1 1 1
Square of Relation
s t u v w
s 2 2 0 0 0
t 2 2 0 0 0
u 0 0 3 3 3
v 0 0 3 3 3
w 0 0 3 3 3
The relation is reflexive
The relation is symmetric
The relation is not anti-symmetric
The relation is transitive
Enter the name of the relation file. Enter quit to exit ==> 5.txt
Could not open the file given. Please enter another file
Enter the name of the relation file. Enter quit to exit ==> bad_file.txt
There must be 2 elements for an edge a, b, c
Could not find element x specified in line x, a
Could not find element y specified in line b, y
Relation on set {a,b,c,d}
Matrix of Relation
a b c d
a 0 0 0 0
b 0 0 0 0
c 0 0 0 0
d 0 0 0 0
Square of Relation
a b c d
a 0 0 0 0
b 0 0 0 0
c 0 0 0 0
d 0 0 0 0
The relation is not reflexive
The relation is symmetric
The relation is anti-symmetric
The relation is transitive
Enter the name of the relation file. Enter quit to exit ==> quit
>>>
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Python 3 Discrete Mathematics We are going to write a program to read in relations, show...
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