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Problem 9 (φ4): Translation between different logics [ Exam: 2018, February 14th]
φ4 = EF([¬a U Gb]∧FG(b))
Solution: EF([¬a U Gb] ∧ FG(b))=EF[¬a SUGb] //Since [a U Gb]∧ FG(b) Is equivalent to [¬a SU Gb].
= EFE[¬a SU Gb]= EFE[¬a SU EGb]
EFE[¬a SU EGb]
My doubt is : as per the comment in the solutions: [a U Gb]∧ FG(b) is equivalent to [¬a SU Gb] but [¬a U Gb] ≠ [a U Gb] (As the former says ¬a holds until always b holds OR ¬a holds forever and the latter says: a holds until always b holds OR a holds forever).
Then how did the substitution happen?
In the comment, a negation symbol is missing. It should be [¬a U Gb]∧ FG(b) Is equivalent to [¬a SU Gb]