The Relation between Sets if I have a relation between A &#x00D7;<!-- × --> A if A

Laurel Yoder 2022-05-21 Answered
The Relation between Sets
if I have a relation between A × A
if A = { 1 , 2 , 3 }
if B = { 1 , 2 , 3 }
R = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) }
can I say that the Relation R is Reflexive and also a Symmetric because I have (a,b) and (b,a) and also (a,a).
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Answers (1)

Mya Hurst
Answered 2022-05-22 Author has 13 answers
Step 1
The definition of the reflexive property is: For every a A ,   a R a.
We see that A = { 1 , 2 , 3 }, and for every variable it relates to itself given that the relation R = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) }.
Definition of antisymmetric is: whenever a , b A are such that aRb and bRa , then necessarily a = b. With A × A, we see with our given R we see that this is antisymmetric.
Step 2
With the definition of symmetric: a , b A ( a R b b R a ), we see that this is symmetric.
So this relation is reflexive, antisymmetric and symmetric.
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