Question 173249
1. W->S
2. U->F
3. (S and F) -> O
4. ~O THEREFORE (~W v ~U)
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5. ~(S and F) .......................... Modus Tollens (using lines 3, 4)


6. ~S v ~F .......................... DeMorgan's Theorem (using line 5)


7. S -> ~F .......................... Material Implication (using line 6)


8. W -> ~F .......................... Hypothetical Syllogism (using lines 1,7)


9. ~F -> ~U .......................... Transposition (using line 2)


10. W -> ~U .......................... Hypothetical Syllogism (using lines 8,10)


11. ~W v ~U .......................... Material Implication (using line 10)