Question

Establish the validity of the argument with the premises p -> (q -> r) , p \/ s , t ->q , ~s and ~r -> ~t

Answer 1

$1. p\to (q\to r)\\ 2. p\vee s\\ 3. t\to q\\ 4. \neg s\\ 5. \neg r\to \neg t\\-----------------\\ 6. p~~~~~(2,4) \text{Disjunctive syllogism}\\ 7. p\to r ~~~~~(1)\text{Hypothetical syllogism}\\ 8. r~~~~~~~(6,7)\text{Modus ponens}\\ 9. t ~~~~(8,5)\text{Modus ponens}\\ 10.q~~~~~(9,3)\text{Modus ponens}\\ 11. q\wedge\neg s~~~~(10,4) \text{Conjunction}\\ \text{The argument is valid}$