Let $$A = \{1, 2, 3, 4\}$$ and $$R : A \rightarrow A$$ be the relation defined by $$R = \{(1,1), (2,3), (3,4), (4,2)\}$$. The correct statement is :

First, we need to check if the relation $$R$$ is a function. A relation from set $$A$$ to set $$A$$ is a function if every element in the domain $$A$$ is mapped to exactly one element in the codomain $$A$$. Here, $$A = \{1, 2, 3, 4\}$$ and $$R = \{(1,1), (2,3), (3,4), (4,2)\}$$.

Examine each element of $$A$$:

For element 1, the pair $$(1,1)$$ maps it to 1, so $$R(1) = 1$$.

For element 2, the pair $$(2,3)$$ maps it to 3, so $$R(2) = 3$$.

For element 3, the pair $$(3,4)$$ maps it to 4, so $$R(3) = 4$$.

For element 4, the pair $$(4,2)$$ maps it to 2, so $$R(4) = 2$$.

Since every element in $$A$$ has exactly one image in $$A$$, $$R$$ is a function. Therefore, option D, which states "R is not a function," is incorrect.

Next, we check if $$R$$ is one-to-one (injective). A function is one-to-one if different inputs produce different outputs, meaning if $$R(a) = R(b)$$, then $$a = b$$.

List the outputs:

$$R(1) = 1$$, $$R(2) = 3$$, $$R(3) = 4$$, $$R(4) = 2$$.

The outputs are 1, 3, 4, and 2, all distinct. Since no two different inputs share the same output, $$R$$ is one-to-one. Therefore, option B, which states "R is not a one to one function," is incorrect.

Now, check if $$R$$ is onto (surjective). A function is onto if every element in the codomain is mapped to by some element in the domain. The codomain is $$A = \{1, 2, 3, 4\}$$.

Check each element:

Is 1 mapped to? Yes, because $$R(1) = 1$$, so 1 is the image of 1.

Is 2 mapped to? Yes, because $$R(4) = 2$$, so 2 is the image of 4.

Is 3 mapped to? Yes, because $$R(2) = 3$$, so 3 is the image of 2.

Is 4 mapped to? Yes, because $$R(3) = 4$$, so 4 is the image of 3.

Since every element in the codomain $$A$$ is an image of some element in the domain, $$R$$ is onto. Therefore, option C, which states "R is an onto function," is correct.

To address option A, since $$R$$ is both one-to-one and onto, it is bijective. A bijective function has an inverse. The inverse function $$R^{-1}$$ can be found by swapping the pairs: $$R^{-1} = \{(1,1), (3,2), (4,3), (2,4)\}$$, which is equivalent to $$R^{-1}(1) = 1$$, $$R^{-1}(2) = 4$$, $$R^{-1}(3) = 2$$, $$R^{-1}(4) = 3$$. This is a valid function, so $$R$$ has an inverse. Therefore, option A, which states "R does not have an inverse," is incorrect.

Hence, the correct answer is Option C.