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Hessinger
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This from Alonzo Church's Mathematical Logic, been stuck on it for a week =(.
14.3 Present a Formal Proof: p [tex]\Rightarrow[/tex] (q [tex]\Rightarrow[/tex] r) [tex]\Rightarrow[/tex] ((p [tex]\Rightarrow[/tex] q) [tex]\Rightarrow[/tex] r)
A truth table has shown that the previous implication is a tautology therefore we should be able to prove it. The first half is easily obtained from modus ponens... p [tex]\Rightarrow[/tex] (q [tex]\Rightarrow[/tex] r) however I have not been able to get ((p [tex]\Rightarrow[/tex] q) [tex]\Rightarrow[/tex] r) any suggestions or guidance would be appreciated.
Homework Statement
14.3 Present a Formal Proof: p [tex]\Rightarrow[/tex] (q [tex]\Rightarrow[/tex] r) [tex]\Rightarrow[/tex] ((p [tex]\Rightarrow[/tex] q) [tex]\Rightarrow[/tex] r)
Homework Equations
The Attempt at a Solution
A truth table has shown that the previous implication is a tautology therefore we should be able to prove it. The first half is easily obtained from modus ponens... p [tex]\Rightarrow[/tex] (q [tex]\Rightarrow[/tex] r) however I have not been able to get ((p [tex]\Rightarrow[/tex] q) [tex]\Rightarrow[/tex] r) any suggestions or guidance would be appreciated.
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