Exam 2018.02.14. ques 5.c.

Question

Hi,

I don't understand the explanation in the screenshot. Could you please explain it in a beginner-friendly way.

Answer 1

I do not really see where I can help here; which of the following sentences of the solution troubles you?

• E[a WU false] is equivalent to EGa
• EGa does not hold in any state since all states that satisfy a, i.e., {s1, s6} have only successor states which do not satisfy a. 
• EGa reduces to false
• the entire formula reduces to (false → ...) which is true, and therefore holds in all states.

Comments

EGa -> AXb
= false -> AXb
= true.
Hence holds in all states.

Got it.
Thanks.