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I have watched Lecture Temporal logics and worked respective exercises. I tried to make use of the formulas in cheatsheet. Please help me with a clear cut appoarch to solve these types of questions.

when it comes to conversion to LTL i follow only the rule removing path quantifiers.
related to an answer for: LTL to LTL
in # Study-Organisation (Master) by (850 points)

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I am afraid that there are no general hints for such exercises. You need some experience with the formulas and have to know a couple of equivalences. The equivalences you need should be listed in the slides, and you can put some on your cheat sheet for the exam. The experience comes with solving many exercises. If you do both, you should be sufficiently prepared for the exam.
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