Answer to Question #232997 in Discrete Mathematics for gikovi

Question

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

Answer 1

SOLUTION

$1.p→(q→r)\\ 2.p∨s\\ 3.t→q\\ 4.¬s \\ 5.¬r→¬t\\ −−−−−−−−−−−−−−−−−\\ 6.p (2,4)Disjunctive \,syllogism\\ 7.p→r (1)Hypothetical\, syllogism\\ 8.r (6,7)Modus \,ponens\\ 9.t (8,5)Modus \,ponens\\ 10.q (9,3)Modus \,ponens\\ 11.q∧¬s (10,4)Conjunction\\ The argument is valid$