Translation logic Q Mistake in 2022.09.06?

Question

Im referring to Problem 9 b in paper 2022.09.06. How did we move from Step 2 to 3, seems like wrong formula was used.

It seems like instead of using Weak Before Formula they seem to have used Strong Before Formula. Is this a mistake on Question / Answer? or Im missing something.

Would Appreciate some help on this please. Thanks

Answer 1

I think that everything is correct. We have the following equivalences: 

• [a SU b] <-> ![(!a) WB b]
•  [a WU b] <-> ![(!a) SB b] 
• [a WB b] <-> [(!b) WU (a&!b)]
• [a SB b] <-> [(!b) SU (a&!b)]
• [a WU b] <-> [b WB (!a & !b)]
• [a SU b] <-> [b SB (!a & !b)]

Note that the negation of a weak operator becomes a strong operator and vice versa, but without negation, it remains the same (either weak or strong).