notes

commit 9c3b215b74ec07fa206f587147a87ba5315c29f7
parent bd75e022744a3333ca8619bba33d018af0e2f984
Author: Andrew <andrewlaack1@gmail.com>
Date:   Tue, 22 Oct 2024 13:47:49 -0500

Took notes about relations

Diffstat:
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Antisymmetric.md
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8
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DiscreteMath.md
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8
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Reflexive.md
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8
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Relation.md
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14
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RelationOnASet.md
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12
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Symmetric.md
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10
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Transitive.md
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8
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7 files changed, 68 insertions(+), 0 deletions(-)
diff --git a/Antisymmetric.md b/Antisymmetric.md
@@ -0,0 +1,8 @@
+:discrete: :math: 
+# AntiSymmetric
+
+Ch 9.1
+
+## Notes
+
+**Definition:** An antisymmetric relation is one such that if xRy then yRx is false where x != y.
diff --git a/DiscreteMath.md b/DiscreteMath.md
@@ -154,3 +154,11 @@ Unit 8.3 (Divide and Conquer)
 
 Unit 8.5 (Inclusion Exclusion)
 	- [PrincipleOfInclusionExclusion](PrincipleOfInclusionExclusion.md)
+
+Unit 9.1 (Relations)
+	- [Relation](Relation.md) (define like function)
+	- [RelationOnASet](RelationOnASet.md) 
+	- [Reflexive](Reflexive.md) 
+	- [Symmetric](Symmetric.md)
+	- [Antisymmetric](Antisymmetric.md)
+	- [Transitive](Transitive.md)
diff --git a/Reflexive.md b/Reflexive.md
@@ -0,0 +1,8 @@
+:discrete: :math: 
+# Reflexive
+
+Ch 9.1
+
+## Notes
+
+**Definition:** A reflexive relation is a relation that is always true for an ordered pair where both elements are the same.
diff --git a/Relation.md b/Relation.md
@@ -0,0 +1,14 @@
+:discrete: :math:
+# Relation
+
+CH 9.1
+
+## Notes
+
+**Definition:** A relation, in math, is a way to describe a connection between elements in the codomain and domain.
+
+Ex:
+
+A -> B
+
+(a,b) in R if a < b.
diff --git a/RelationOnASet.md b/RelationOnASet.md
@@ -0,0 +1,12 @@
+:discrete: :math: 
+# Relation on a Set
+
+Ch 9.1
+
+## Notes
+
+**Definition:** A relation on a set is a relation where the domain and the codomain are the same set.
+
+Ex:
+
+Defin the relation R as the relation from A -> A for (a,b) such that a < b.
diff --git a/Symmetric.md b/Symmetric.md
@@ -0,0 +1,10 @@
+:discrete: :math: 
+# Symmetric
+
+Ch 9.1
+
+## Notes
+
+**Definition:** A symmetric relation is a relation such that if xRy then yRx for all (x,y). 
+
+For a symmetric relation to imply it is reflexive, the domain and the codomain must be the same. 
diff --git a/Transitive.md b/Transitive.md
@@ -0,0 +1,8 @@
+:discrete: :math: 
+# Transitive
+
+Ch 9.1
+
+## Notes
+
+**Definition:** A transitive relation holds the transitive property namely that if xRy and yRz then xRz for all x,y,z.