Establish the validity of the argument with the premises p -> (q -> r) , p \/ s , t ->q , ~s and ~r -> ~t
SOLUTION
1.p→(q→r)2.p∨s3.t→q4.¬s5.¬r→¬t−−−−−−−−−−−−−−−−−6.p(2,4)Disjunctive syllogism7.p→r(1)Hypothetical syllogism8.r(6,7)Modus ponens9.t(8,5)Modus ponens10.q(9,3)Modus ponens11.q∧¬s(10,4)ConjunctionTheargumentisvalid1.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 valid1.p→(q→r)2.p∨s3.t→q4.¬s5.¬r→¬t−−−−−−−−−−−−−−−−−6.p(2,4)Disjunctivesyllogism7.p→r(1)Hypotheticalsyllogism8.r(6,7)Modusponens9.t(8,5)Modusponens10.q(9,3)Modusponens11.q∧¬s(10,4)ConjunctionTheargumentisvalid
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