The correct option is A xRy⇔|x|=|y|
Let's consider xRy⇔|x|=|y|
Now, |x|=|x|
⇒xRx
Hence, R is reflexive.
Now, let xRy ⇒|x|=|y|
or |y|=|x| as equality commutative
⇒yRx
Hence, R is symmetric.
Checking for transitive,
Let (x,y) and (y,z) satisfies R
Now, xRy,yRz
⇒|x|=|y|,|y|=|z|
⇒|x|=|z|
⇒xRz
∴(x,z) satisfies R
Hence, R is transitive.
Hence, R is an equivalence relation.
R is not symmetric relation as 3≥2 does not implies 2≥3. Hence R is not an equivalence relation.
R is not symmetric relation as 3>2 does not implies 2>3. Hence R is not an equivalence relation.
R is not symmetric relation as 1<3 is true but 3<1 is not true. Hence R is not an equivalence relation.