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July 14th, 2017, 02:16 PM   #1
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Question Need discrete math homework help. Logic.

Sorry if this is the wrong sub-thread. I am a self-taught programmer, and have been learning discrete math (for algorithms) from a text book: Discrete Mathematics and its Applications, 6th edition.

I usually don't have trouble with the material, but there is a particular question in the chapter on logic:

"32. show that the equivalence p∧¬p≡F can be derived using resolution together with the fact that a conditional statement with a false hypothesis is true [Hint: let q = r = F in resolution.]"

I am totally lost, what am I supposed to do here?

Last edited by skipjack; July 14th, 2017 at 02:33 PM.
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July 14th, 2017, 02:45 PM   #2
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Have you read this?
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July 14th, 2017, 03:33 PM   #3
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Quote:
Originally Posted by skipjack View Post
Have you read this?
I understand everything until he has three clauses, p and not p, and the literal value. I don't understand "the empty clause" or know what he is talking about. Does he mean the empty string, lambda? Resolution uses two variables, but p, is one variable. It seems like he is saying (p v λ) ^ (¬p v λ) therefore (λ v λ). And since lambda is empty then it is a contradiction, somehow? That is valid?

Last edited by chris7789; July 14th, 2017 at 03:38 PM.
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July 14th, 2017, 03:44 PM   #4
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Would this also work for an appropriate answer:

q = r = F;
(p∨q) ∧(¬p∨r) ≡
(¬p⇒q) ∧(p⇒r) ≡
T∧F ≡p∧¬p≡F
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