If 
is the set of integers and if the relation 
is defined over 
by 
, iff 
is an even integer, 
, the relation 
is
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
is an even integer, 
is reflexive relation.
Let 
is an even integer.
is symmetric relation.
Now, let 
and 
Then, 
is an even integer and 
is an even integer.
is an even integer.
and 
.
So, 
is transitive relation.
Hence, 
is an equivalence relation.
A relation 
on given set 
is said to be anti-symmetric iff 
and 
.
∴ Given relation is not anti-symmetric relation.
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