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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