SOLUTION: Hi could anyone help me with this proof? 1. V v H 2. ~(V & D) 3. ~(D & H) / ~(D & O) Thank you!

Algebra ->  Proofs -> SOLUTION: Hi could anyone help me with this proof? 1. V v H 2. ~(V & D) 3. ~(D & H) / ~(D & O) Thank you!      Log On


   

Question 981101: Hi could anyone help me with this proof?
1. V v H
2. ~(V & D)
3. ~(D & H)
/ ~(D & O)
Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
NumberStatementLines UsedReason
1V v H
2~(V & D)
3~(D & H)
:.~(D & O)
4H v V1Commutation
5~~H v V4Double Negation
6~H -> V5Material Implication
7~V v ~D2De Morgan's Law
8~~V -> ~D7Material Implication
9V -> ~D8Double Negation
10~H -> ~D6,9Hypothetical Syllogism
11~D v ~H3De Morgan's Law
12~~D -> ~H11Material Implication
13D -> ~H12Double Negation
14D -> ~D13,10Hypothetical Syllogism
15~D v ~D14Material Implication
16~D15Tautology
17~D v ~O16Addition
18~(D & O)17De Morgan's Law