Implements all methods

equivalence-relation/projeto-logica-unifacisa/BinaryRelationUtils.py

@@ -17,7 +17,11 @@ def verify_reflexivity(binary_relation, input_set):
         Return True if the binary relation in the given input set is reflexive
         or False if it is not.
         """
-        # TODO: Replace line below with actual code.
+        for x in input_set:
+            if (x, x) not in binary_relation.relation(input_set):
+                return False
+
+        return True
         pass
 
     @staticmethod
@@ -33,7 +37,13 @@ def verify_symmetry(binary_relation, input_set):
         Return True if the binary relation in the given input set is symmetric
         or False if it is not.
         """
-        # TODO: Replace line below with actual code.
+        relation = binary_relation.relation(input_set)
+        for x in input_set:
+            for y in input_set:
+                if(x, y) in relation and (y, x) not in relation:
+                    return False
+
+        return True
         pass
 
     @staticmethod
@@ -49,7 +59,15 @@ def verify_transitivity(binary_relation, input_set):
         Return True if the binary relation in the given input set is transitive
         or False if it is not.
         """
-        # TODO: Replace line below with actual code.
+        relation = binary_relation.relation(input_set)
+
+        for x in input_set:
+            for y in input_set:
+                for z in input_set:
+                    if (x, y) in relation and (y, z) in relation and (x, z) not in relation:
+                        return False
+
+        return True
         pass
 
     @staticmethod
@@ -62,10 +80,16 @@ def verify_antisymmetry(binary_relation, input_set):
 
         input_set - A set closed under the binary relation.
 
-        Return True if the binary relation in the given input set is 
+        Return True if the binary relation in the given input set is
         antisymmetric or False if it is not.
         """
-        # TODO: Replace line below with actual code.
+        relation = binary_relation.relation(input_set)
+
+        for x, y in relation:
+            if (y, x) in relation and x != y:
+                return False
+
+        return True
         pass
 
     @staticmethod
@@ -78,10 +102,10 @@ def verify_equivalency(binary_relation, input_set):
 
         input_set - A set closed under the binary relation.
 
-        Return True if the binary relation in the given input set is 
+        Return True if the binary relation in the given input set is
         an equivalence relation or False if it is not.
         """
-        # TODO: Replace line below with actual code.
+        return BinaryRelationUtils.verify_reflexivity(binary_relation, input_set) and BinaryRelationUtils.verify_symmetry(binary_relation, input_set) and BinaryRelationUtils.verify_transitivity(binary_relation, input_set)
         pass
 
     @staticmethod
@@ -98,5 +122,20 @@ def get_partitioning(binary_relation, input_set):
 
         Return None if the binary relation is not an equivalence relation or a partitioning of the input set (e.g.: [{1, 3, 5, ...}, {2, 4, 6, ...}]) if it is an equivalence relation.
         """
-        # TODO: Replace line below with actual code.
-        return []
+        return_list = []
+
+        relation = binary_relation.relation(input_set)
+
+        if BinaryRelationUtils.verify_equivalency(binary_relation, input_set):
+            for x in input_set:
+                partition = set()
+                for y in input_set:
+                    if (x, y) in relation:
+                        partition.add(y)
+
+                if partition not in return_list:
+                    return_list.append(partition)
+
+            return return_list
+        else:
+            return None

equivalence-relation/projeto-logica-unifacisa/GreaterThanBinaryRelation.py

@@ -7,15 +7,7 @@ class GreaterThanBinaryRelation(BinaryRelation):
     """A Binary Relation which elements in an ordered pair share the same first letter."""
 
     def contains_ordered_pair(self, x, y):
-        """
-        This method returns a boolean value indicating if the first element of a given ordered pair is greater than the second one.
-
-        Arguments:
-        x - The first element of the ordered pair.
-        y - The second element of the ordered pair.
-
-        Return True if the first element of the ordered pair is greater than the second element, otherwise, return False.
-        """
+        return x > y
         pass
 
     def relation(self, S):
@@ -27,4 +19,6 @@ def relation(self, S):
 
         Return a set of pairs in SxS (a.k.a. S²) that belong to the binary relation.
         """
+
+        return set([(x, y) for x in S for y in S if self.contains_ordered_pair(x, y)])
         pass

equivalence-relation/projeto-logica-unifacisa/SameFirstLetterBinaryRelation.py

@@ -16,6 +16,7 @@ def contains_ordered_pair(self, x, y):
 
         Return True if the ordered pair belongs to the binary relation, otherwise, return False.
         """
+        return x[0] == y[0]
         pass
 
     def relation(self, S):
@@ -27,4 +28,5 @@ def relation(self, S):
 
         Return a set of pairs in SxS (a.k.a. S²) that belong to the binary relation.
         """
+        return set([(x, y) for x in S for y in S if self.contains_ordered_pair(x, y)])
         pass

equivalence-relation/projeto-logica-unifacisa/SameParityBinaryRelation.py

@@ -18,6 +18,13 @@ def contains_ordered_pair(self, x, y):
 
         Return True if the ordered pair belongs to the binary relation, otherwise, return False.
         """
+
+        if x % 2 == 0 and y % 2 == 0:
+            return True
+        elif x % 2 != 0 and y % 2 != 0:
+            return True
+        else:
+            return False
         pass
 
     def relation(self, S):
@@ -29,4 +36,5 @@ def relation(self, S):
 
         Return a set of pairs in SxS (a.k.a. S²) that belong to the binary relation.
         """
+        return set([(x, y) for x in S for y in S if self.contains_ordered_pair(x, y)])
         pass