SOLUTION: COMPLETE THE FOLLOWING PROOFS WITHOUT USING CONDITIONAL PROOF OR INDIRECT PROOF Premises: 1. T ∨ (P ∨ S) 2. ~T 3. P ⊃ Q 4. ~T ⊃ (S ⊃ L) Conc

Question 1029119: COMPLETE THE FOLLOWING PROOFS WITHOUT USING CONDITIONAL PROOF OR
INDIRECT PROOF
Premises:
1. T ∨ (P ∨ S)
2. ~T
3. P ⊃ Q
4. ~T ⊃ (S ⊃ L)
Conclusion: Q V L
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
1. T ∨ (P ∨ S)-----------------Hypothesis
2. ~T ------------------Hypothesis
3. P ∨ S ------------------Disjunctive syllogism on #1 and #2
4. ~T ⊃ (S ⊃ L) ---------------Hypothesis
5. S ⊃ L ---------------modus ponens on #2 and #4
6. ~~P∨S --------------double negation on #3
7. ~P⊃S ---------------material implication on #6
8. ~P⊃L-------------- hypothetical syllogism on #5 and #7
9. ~L⊃P --------------contrapositive of #8
10. P⊃Q --------------Hypothesis
11. ~L⊃Q -------------hypothetical syllogism on #9 and #10
12. ~~L∨Q -------------material implication on #11
13. L∨Q -------------double negation
14. Q∨L --------------commutativity

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SOLUTION: COMPLETE THE FOLLOWING PROOFS WITHOUT USING CONDITIONAL PROOF OR INDIRECT PROOF Premises: 1. T ∨ (P ∨ S) 2. ~T 3. P ⊃ Q 4. ~T ⊃ (S ⊃ L) Conc