Let 
. Let R be a relation on A defined by 
if and only if 
. Let 
be the number of elements in R and 
be the minimum number of elements required to be added in R to make it a reflexive relation. Then 
is equal to
Text Solution
Verified by ExpertsA
The relation 
is defined for the set 
with the condition 
. Let's determine the pairs 
that satisfy this condition.
For 
:
Solving 
, we find 
.
For 
:
Solving 
, we find 
.
For 
:
Solving 
, we find 
.
For 
:
Solving 
, we find
For 
:
Solving 
, we find
For 
:
Solving 
, we find 
.
The relation 
consists of the following pairs:
}
Currently, 
has 
elements. To make 
reflexive, it must include all pairs ( 
) for every 
. We identify the missing reflexive pairs 
, and 
, which are required to satisfy reflexivity.
Thus, 
more elements are needed.
Therefore, the total 
.
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