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In propositional logic, if $(P→Q)\wedge (R→S)$ and $(P\vee R)$ are two premises such that $Y$ is the premise:

$\begin{array}{c}( P \rightarrow Q) \wedge ( R \rightarrow S) \\ P \vee R \\ \hline \\ Y \\ \hline \end{array}$

  1. $P\vee R$
  2. $P\vee S$
  3. $Q\vee R$
  4. $Q\vee S$
asked in CBSE/UGC NET by Active (3.9k points) | 1.8k views

Given that 



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)

plz explain a little.. i know propositions. but i could not understand what the question is saying.. what are the operators between



totally unclear question to me
Y is not premise it should be conclusion

1 Answer

+3 votes
Best answer

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)

answered by Veteran (50k points)
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