In propositional logic, if $(P→Q)\wedge (R→S)$ and $(P\vee R)$ are two premises such that $Y$ is the premise:
$\begin{array}{c}( P \rightarrow Q) \wedge ( R \rightarrow S) \\ P \vee R \\ \hline \\ Y \\ \hline \end{array}$
Given that
(P→Q)˄(R→S)
(P˅R)
here if P then Q and if R then S now P V R means either Q is true or S is true
so Y will be Q V S so ans is 4)
Given that premises are
(P→Q) = ~PVQ
(R→S) = ~RVS
Q V S
There will be Resolution (rule of inference ) between these premises to give conclusion
~ P & P , R & R' will resolve out and then we construct the disjunction of the remaining clauses
to give SVQ option 4)
Gatecse