Functions

The correct answer is A:reflexive
Given that;
R is a relation on N defined by;

⇒
The given equation is reflexive if x=a and y=a
i.e., and symmetric
satisfies the equation (i)




Not symmetric
Let us assume the function is transitive for (9,1)
Let's Substitute and test

Hence, not transitive

and
Let




or
which is the inverse of is the map g.
Range

Given that,
be a binary operation on the set of rational numbers
and
By inspection, we get ?4? is the identity elements with respect to operation
Let ,
where is identity element






Hence, identity element

Answer (a) symmetric

Answer (c)

Answer (d) an equivalence relation

Answer (a)

Answer (c) 2