3. Let A = {1, 2, 3}, let S = P(A) and let RC S x S be a relation defined by the rule (X,Y) ER⇒ (XnY=0)A (XUY = A). (a) Prove or find a counterexample for the following properties: • antisymmetry • asymmetry. symmetry. • irreflexivity/ • reflexivity. • transitivity • uniqueness (b) Based on the findings from the previous point, conclude whether R is a graph, partially ordered set, equivalence relation, or a function (several answers may hold simultaneously). Analyze the relation R.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 52E
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3. Let A = {1, 2, 3}, let S = P(A) and let RC S x S be a relation defined by the rule
(X,Y) ER⇒ (XnY=0)A (XUY = A).
(a) Prove or find a counterexample for the following properties:
· antisymmetry.
asymmetry.
• symmetry.
● irreflexivity/
• reflexivity.
• transitivity
• uniqueness
(b) Based on the findings from the previous point, conclude whether R is a graph, partially ordered
set, equivalence relation, or a function (several answers may hold simultaneously). Analyze the
relation R.
Transcribed Image Text:3. Let A = {1, 2, 3}, let S = P(A) and let RC S x S be a relation defined by the rule (X,Y) ER⇒ (XnY=0)A (XUY = A). (a) Prove or find a counterexample for the following properties: · antisymmetry. asymmetry. • symmetry. ● irreflexivity/ • reflexivity. • transitivity • uniqueness (b) Based on the findings from the previous point, conclude whether R is a graph, partially ordered set, equivalence relation, or a function (several answers may hold simultaneously). Analyze the relation R.
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