Gate Discrete

Question

Prove that the premises p → q ,p → r, q → ~ r , p are inconsistent.

Answer 1

defn of inconsistency:

THE CONJUCTION OF ALL THE PREMICES IS FALSE

SO (P-->Q)^(P-->R)^(Q-->R')^P

   =(P'+Q)(P'+R)(Q'+R')(P)

   =(P'+P'R+P'Q+QR)(Q'+R')(P)

   =(P'+QR)(Q'P+R'P)

  =P'Q'P+P'R'P+QRQ'P+QRR'P

 =0+0+0+0=0 =FALSE

IT IS AN INCONSISTENCY