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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) | 1.4k views
0

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)

0
plz explain a little.. i know propositions. but i could not understand what the question is saying.. what are the operators between

(P→Q)˄(R→S)

    (P˅R)

totally unclear question to me
0
Y is not premise it should be conclusion

1 Answer

+3 votes
Best answer

Given that premises are

 (P→Q)˄(R→S)

 (P˅R) 

   (P→Q)   = ~PVQ

   (R→S)  = ~RVS

   (P˅R) 


  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 Boss (48.2k points)
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