Consider the following relations:
are integers such that
then
is an equivalence relation but is not an equivalence relation
neither nor is an equivalence relation
is an equivalence relation but is not an equivalence relation
and both are equivalence relations
As we learnt in
Equivalence relation -
Any relation which is reflexive, symmetric and transitive is called an equivalence relation
-
given that qm = pn ,
Is is always true for (a, a) reflexive.
x = - 1
{0, -1}
Correct option is 4.
Option 1)
is an equivalence relation but is not an equivalence relation
This is an incorrect option.
Option 2)
neither nor is an equivalence relation
This is an incorrect option.
Option 3)
is an equivalence relation but is not an equivalence relation
This is an incorrect option.
Option 4)
and both are equivalence relations
This is the correct option.
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