Some clarification of the question if needed:

I need to find a rule by which different alternatives are ranked by that rule. For example: ??$x\succeq y$?? if and only if ??$x\geq y$?? . It can be verified that this preference relation is both monotone and convex, so this is not an answer to this question 2.c.

Also if I give a preference relation and claim that it is not convex, then I must establish this properly: I must show that it fails the definition of convexity. Alternatively, if I claim that it is monotone, then I must verify that the definition is satisfied.

2. Provide an example of a preference relation _ over R+ (i.e., when there is a single good): (a) Which is not convex. (b) Which is locally nonsatiated but not monotone. (c) Which is strongly monotone but not convex