The binary relation R = {(0,0,(1,1)} on A = {1,2,3} is Reflexive, Not Symmetric, Transitive Not Reflexive, Symmetric, Transitive Reflexive, Symmetric, Not Transitive Reflexive, Not Symmetric, Not Transitive
Answers
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Answer:
Given : The binary relation R = {(0,0,(1,1)} on A = {1,2,3}
To find : The relation is satisfying or not and explain all terms?
Solution :
This is not the relation from set A→ A
Since relation R contains 0 but set does not contain element 0.
Hence,this relation is incorrect.
Reflexive: A relation is reflexive if all (x,x) belongs to relation R where x belongs to set A.
Irreflexive: A relation is irreflexive if all (x,x) does not belong to relation R where x belongs to set A.
R={(1,2),(3,4)} on set A is irreflexive while
R={(1,1)} on set A is not irreflexive.
Symmetric: A relation is symmetric if for all a,b belonging to set A if (a,b) belongs to relation then (b,a) also belongs to relation where a,b belongs to set A.
R={(1,1)} is symmetric
R={(2,3)} is not symmetric as (2,3) belongs to relation R but (3,2) does not belong to relation R.
Transitive: A relation is transitive if for all a,b,c belongs to set A such that if (a,b) and (b,c)belongs to relation R then (c,a) also belongs to relation R.
R={(1,2),(2,3),(3,1)} is transitive
R={(1,1),(1,2),(2,1)} is not transitive because (2,1) and (1,2) belongs to relation R but (2,2) does not belong to relation R .
Equivalence: A relation is said to be equivalence if the relation is reflexive, symmetric and transitive.