Give an example of a relation on the set A with 4 elements which is reflexive, but not transitive.
Let $A = \{1, 2, 3, 4, 5 ,6\}$ be the set with 6 elements.
I have worked out the relation $R = \{(1,1),(2,4),(4,2),(5,5)\}$
I believe this is reflexive because they are all elements of A but not not transitive as $2,4 4,2$ are there but not $4,4$.
Is this correct?
Consider the relation R on the above set given as :
$R={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(4,2),(2,6)}$
For every element $a$ in $A$ we have $(a,a)$ in $R$ hence it is reflexive, but also $(4,2)$ and $(2,6)$ belongs in $R$ but not $(4,6)$ hence it is not transitive