SOLUTION: I can't seem to get to solve this proof. 1. W->S 2. U->F 3. (S and F) -> O 4. ~O THEREFORE (~W v ~U)

Algebra ->  Proofs -> SOLUTION: I can't seem to get to solve this proof. 1. W->S 2. U->F 3. (S and F) -> O 4. ~O THEREFORE (~W v ~U)      Log On


   

Question 173249: I can't seem to get to solve this proof.
1. W->S
2. U->F
3. (S and F) -> O
4. ~O THEREFORE (~W v ~U)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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)