in Mathematical Logic
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premises are -

A

A → ( B ∨ C )

B → ¬A

conclusion -

C

 

is valid or not ?
in Mathematical Logic
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4 Comments

Bhuv kumar if we can't infer A --> C from these premises than
(A^ (A → ( B ∨ C )) ^ (B → ¬A) ) → ( A → C) Then this should be false Isn't?
But this seem to be true to me. Correct me if I'm wrong.
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bro @ hemant @ bhuv both A->C or only C can be inferred from given question since if lhs true then rhs can never be false forboth cases
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yes bro that is what i'm saying. :)
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1 Answer

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Best answer

solution Approach:

the premise can be written as

A^[A->(BᐻC)]^[B->~A] => C

so to say its not valid prove That the left hand side can be Assigned a True value and Right hand side as False then the Premises are not valid.

So C=False

A=True

So B can be True or False  in both the cases the right hand side can't be True So the premise is Valid 

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