Transition systems that satisfy LTL but not CTL, and vice versa

Question

I am learning about temporal logic and model checking systems. One conceptual exercise that I am struggling with is how to create a transition system which satisfies only one of two given properties, when one is in LTL and one is in CTL. For example:

• Find a transition system that satisfies only one of the following two properties: $FGp$, $AFEGp$
• Find a transition system that satisfies only one of the following two properties: $FGp$, $EFEGp$
• Find a transition system that satisfies only one of the following two properties: $GFp$, $AGEFp$

How should I begin when trying to reason about these types of problems? In general, is it easier to design transition systems for LTL properties or CTL properties? Or does it depend on the situation?

Any insight would be appreciated!