SOLUTION: 1. (⌐SvL)→F, ⌐[P v (QvS)] Ⱶ F 2. ⱵS → (B→S)

Algebra ->  Proofs -> SOLUTION: 1. (⌐SvL)→F, ⌐[P v (QvS)] Ⱶ F 2. ⱵS → (B→S)       Log On


   

Question 1042510: 1. (⌐SvL)→F, ⌐[P v (QvS)] Ⱶ F
2. ⱵS → (B→S)



Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1. (⌐SvL)→F -------------hypothesis
2. ~(~SvL)vF --------------------material implication
3. (S&~L)vF --------------------de Morgan's and double negation
4. (SvF)&(~LvF) -----------------distributivity
5. SvF ------------------------simplification
6. ~(~S)vF ----------------------double negation
7. ~S -> F ---------------------material implication
8. ⌐[P v (QvS)]----------------hypothesis
9. ~P &~Q & ~S ------------------de Morgan's on #8
10. ~S -------------------------simplification
11. F -------------------------modus ponens on #7 and #11

1. S -> (B-> S)----------------hypothesis
2. ~S v (~B v S) --------------material implication (twice)
3. ~S v (S v ~B) --------------commutativity
4. (~S v S) v ~B --------------associativity
5. T v ~B ---------------------tautology (law of excluded middle)
6. T -----------------------tautology