Let’s make a truth table for this problem: R->~P, Q,
Q->(Pv~S) 
S->~R
|
P |
Q |
R |
S |
~P |
~R |
~S |
Pv~S |
R->~P |
Q->(Pv~S) |
R->~P, Q, Q->(Pv~S) |
S->~R |
|
T |
T |
T |
T |
F |
F |
F |
T |
F |
T |
F |
F |
|
T |
T |
T |
F |
F |
F |
T |
T |
F |
T |
F |
T |
|
T |
T |
F |
T |
F |
T |
F |
T |
T |
T |
T |
T |
|
T |
T |
F |
F |
F |
T |
T |
T |
T |
T |
T |
T |
|
T |
F |
T |
T |
F |
F |
F |
T |
F |
T |
F |
F |
|
T |
F |
T |
F |
F |
F |
T |
T |
F |
T |
F |
T |
|
T |
F |
F |
T |
F |
T |
F |
T |
T |
T |
F |
T |
|
T |
F |
F |
F |
F |
T |
T |
T |
T |
T |
F |
T |
|
F |
T |
T |
T |
T |
F |
F |
F |
T |
F |
F |
F |
|
F |
T |
T |
F |
T |
F |
T |
T |
T |
T |
T |
T |
|
F |
T |
F |
T |
T |
T |
F |
F |
T |
F |
F |
T |
|
F |
T |
F |
F |
T |
T |
T |
T |
T |
T |
T |
T |
|
F |
F |
T |
T |
T |
F |
F |
F |
T |
T |
F |
F |
|
F |
F |
T |
F |
T |
F |
T |
T |
T |
T |
F |
T |
|
F |
F |
F |
T |
T |
T |
F |
F |
T |
T |
F |
T |
|
F |
F |
F |
F |
T |
T |
T |
T |
T |
T |
F |
T |
If an argument is valid, then every assignment where the premises are all true is also an assignment where the conclusion is true. As you can see from the above table, it’s always the case that when the antecedent (R->~P, Q, Q->(Pv~S)) is true the succedent (S->~R) is also true. Therefore, this sequent is valid.