Option (B):
Take P = True and Q = False
$(p\rightarrow q) = (T\rightarrow F) = F$
This will make whole L.H.S equal to FALSE, And ‘$F\rightarrow$ Anything’ will be TRUE
Thus, we can eliminate Option (A)
Now we’ll try to make this statement False
For that we need L.H.S = T & R.H.S = F
Take P = Q = R = S = FALSE
$\left \{ (F\rightarrow F) \wedge (T\vee F)\wedge (F\rightarrow F) \right\}\rightarrow \sim(F\rightarrow F)$
Which will result in, $T\rightarrow F$ = $F$
Thus, we can also eliminate Options (C)
And since we can get both True and False values for the given predicate, It is Satisfiable.