To determine whether $R1$ and $R2$ are injective, surjective, or functions at all, we need to first check if they satisfy the definition of a function.

Definition of a function:

A relation is a function if every element in the domain (set $S$) is mapped to exactly one element in the codomain. Specifically, for each element $x$ in the domain, there must be one and only one pair $(x, y)$ in the relation.

Relation $R1$:

• Relation $R1$ = {(Feb, Feb), (March, April), (April, March), (March, March)}

1. Is $R1$ a function?
   • The domain of the relation $R1$ should contain all elements from $S$. Let's check:
     • $S = \{\text{Jan}, \text{Feb}, \text{March}, \text{April}, \text{May}\}$
     • In $R1$, we have Feb, March, and April as elements of the domain, but Jan and May are missing.
     • Additionally, March