0
  • A = {Q↔(¬(R→(S∧¬Q))→R) , R , S∨Q}
  • B = {¬(R∧¬S) , ¬S→Q , R→¬Q , ¬R→R}
  • Γ = {R∨(Q→S) , ¬(R∧¬Q) , ¬R→¬S}
  • Δ = {¬R∨S , S∨¬S , ¬Q↔R , R ↔ (P∨¬P)}

From one of the consistent sets Q follows, from one of them ¬Q follows, and from one of them neither Q nor ¬Q follows. State which is which.

I'm not asking for an answer. I don't understand what it means that "Q follows" or "¬Q follows."

I saw this post: Sentential Logic Help? but I didn't quite understand his explanation.

Community
  • 1
K.Wong
  • 11

1 Answers1

0

Q ($\lnot$Q) will "follow" from the set of premises S if there is no instance where we have all of the members of S true, but Q ($\lnot$Q) is false.

Perhaps a more clear word for the idea here would be 'producible'. Q ($\lnot$Q) will qualify as producible from the set of premises S if given all of the members of S as true, and an adequate set of sound rules of inference/axioms, then Q ($\lnot$Q) can get produced.

For instance, say we have the following set:

{(J$\rightarrow$K), (J$\land$Q)}

Then, (K$\land$Q) is producible, or can get said to "follow" from the above set, since it can follow from assuming all of the members of above set.

Doug Spoonwood
  • 11,211