**For this assignment, you will write a C++ program to input relations on a set, S, and then determine whether each relation is reflexive, symmetric, antisymmetric, transitive, a partial order, or an equivalence relation.**

**Your program must read from a file via cin using input redirection. The structure of the data file will be as follows.**

**The first line of the file indicates how many relations are in the file.****Each relation begins with a line containing two integers. The first of these integers,***m*, give the size of*S*= {*0,*...,*m*-1}, and the second,*n*, give the number of ordered pairs in the relation. The next*n*lines will each contain one ordered pair of integers from the set*S*.**You may use this getRelation function to read a relation into an adjacenty matrix. Your program must include functions**.*isReflexive*,*isSymmetric*,*isAntisymmetric*, and*isTransitive*

**EXAMPLE INPUT
2
4 5
1 2
0 2
2 1
0 0
2 0
3 3
1 1
2 2
0 0**

**EXAMPLE OUTPUT
#1:
REFLEXIVE - no
SYMMETRIC - yes
ANTISYMMETRIC - no
TRANSITIVE - no
PARTIAL ORDER - no
EQUIVALENCE RELATION - no**

**#2:
REFLEXIVE - yes
SYMMETRIC - yes
ANTISYMMETRIC - yes
TRANSITIVE - yes
PARTIAL ORDER - yes
EQUIVALENCE RELATION - yes **

**TEST DATA: relationsData.txt**

**DUE: Wed, April 03, at the beginning of class. You must include a signed and dated integrity statement at the beginning of your code. Append to your source code a run of your program that uses relationsData.txt as input. Also, place your C++ code (NOT your Visual Studio project) in your Drop Folder at P:\Public\CmpSc 360 Spring 2013\DROP FOLDERS. (P: is your instructor's (clb8) shored public drive.)**