GO Classes 2023 | Weekly Quiz 5 | Question: 8

In the video, everything is crystal clear.

(R’ + F’) → (S.L)

S → T

T’ 

then 

R

take R = false then T = false, S = false now at this point :

(T + F’) → F.L ≈ T → F which is invalid.

Hence, Our initial assumption is wrong → R = true

@JAINchiNMay always think like this in these types of problems, it will be easy for you.

@JAINchiNMay Actually if the 3 conditions are met, then it rained as well as it was foggy. This will help you:-

rain’+fog’ → race . life   (i)

race → trophy          (ii)

trophy’                       (iii)

Eqn (ii) can be rewritten as : trophy’ → race’  [if no trophy then no race, contrapositive]

It is given in eqn (iii) that there was not trophy. [Hence we can conclude no race]  (iv)

Now eqn (i) can be rewritten as: (race . life)’ → (rain’ + fog’)’

                                                  or, race’ + life’ → rain . fog [ means, if either no race or no life saving,                                                                                                         then  both rain and fog]

And we already concluded no race in eqn (iv), hence there was both rain and fog.

Option A.