Question 746251: What is the proof of:
1. D horseshoe Q
2. ~D v ~Q
/ ~D
Answer by tinbar(133)   (Show Source):
You can put this solution on YOUR website! I assume horseshoe means "AND" just like v means "OR"
So from 1) D AND Q you know both D and Q must be true, confirm this by looking up the truth table for the binary "AND" relationship.
So we can break 1 into 1a) and 1b) where 1a) is D and 1b) is Q
So now I have:
1a) D
1b) Q
2) ~D OR ~Q
Show ~D
Now from 1b) Q is true, so for 2) to be true, ~D MUST be true.
Why? In general, if you say (A OR B) is true, then the OR truth table says at least one of A, B is true. But now suppose we know the overall statement (A OR B) evaluates to true, but we also know that B is false, that is we have ~B. Well if B is false, but (A OR B) is true, then the truth table for OR tells us the only way this can happen is if A is true. So in short if you are given (A OR B) as well as ~B, then you conclude A is true. Similarly if you are given (A OR B) as well as ~A, then you conclude B must be true.
Now I have used this same logic to prove your result. With a similar argument you can actually show ~Q as well. Try it out!
When you are actually writing up the proof, you must quote each rule. I have simply given you an outline. Look at http://www.simplyquality.org/Logic.htm for a set of the basic rules. All the rules you require are in there.
Good luck!
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