Question

Prove that the premises P → Q, Q → R, S → ¬R and P ∧ S are inconsistent.

Answer 1

From $P\land S$ we conclude P=T,S=T. From $P=T,P\to Q$ we conclude $Q=T$ . From $Q=T,Q\to R$ we conclude $R=T$ . From $S=T,S\to \lnot R$ we conclude $\lnot R=T\Rightarrow R=F$ . We have a contradiction. The premises are inconsistent.