Answer:
(I) Yes
(II) Yes
(III) No
(IV) No
Step-by-step explanation:
(I) The relation is a function from A to A as it satisfies both existence and uniqueness: every element of A (domain) is related to only one element of A (codomain).
(II) The relation is an everywhere defined function as every element of A is related to an element of A.
(III) The relation is not an onto (surjective) function.
Let's recall the definition of an onto function:
An onto function f : A -> B satisfies: [tex]\forall y \in B : \exists x \in A / f(x)=y[/tex].
In this case, [tex]\nexists x \in A / xRc[/tex]. So, the function is not onto.
(IV) The relation is not a one to one (injective) function.
Let's recall the definition of a one to one function:
A one to one function f : A -> B satisfies: [tex]x \neq y \Rightarrow f(x) \neq f(y)[/tex].
In this case, both [tex]b[/tex] and [tex]f[/tex] relate to [tex]e[/tex], so the function is not one to one.
