The number of relations on the set 
, containing at most 6 elements including 
, which are reflexive and transitive but not symmetric, is ______.
Text Solution
Verified by Experts6
(6)
Since relation needs to be reflexive the ordered pairs 
need to be there and 
is also to be included.
Let's call 
the base relation.
contain 
ordered pairs, remaining 5 ordered are
We have to add at most two ordered pairs to 
such that resulting relation is reflexive, transitive but not symmetric.
Following are the only possibilities.
OR 
OR 
OR 
OR 
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