on 
defined by 
, iff 
on 
defined by 
, iff 
and 
on 
defined by 
, iff 
. Find whether relation 
and 
are reflexive, symmetric and transitive.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
We have, 
, iff 
, where 
.
For relation 
Reflexivity : Let 
(reflexive)
Symmetry: 
is symmetric.
Transitivity: 
but 
(not transitive)
We have 
, iff 
, where 
For relation 
Reflexivity : 
and 
(not reflexive)
Symmetry: 
is symmetric.
Transitivity: 
but 
.
is not transitive.
For relation 
We have, 
,
iff 
, where 
Reflexivity: 
is reflexive.
Symmetry: Let 
,
we get 
and 
and if 
, we get 
and 
.
is not symmetry.
Transitivity: We have, 
as 
and 
is not transitive.
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