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millani
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How do I prove this? (propositional logic)
How to prove this
[itex](p \rightarrow (q \vee p)) \rightarrow r \vdash \neg p \vee (q \vee r)[/itex]
using only the natural deduction rules in propositional logic?
http://en.wikipedia.org/wiki/Propositional_logic
(natural deduction rules only)
[itex]1: (p \rightarrow (q \vee p)) \rightarrow r[/itex] premise
<start of hypothesis 0> ; I tried to make a box here but failed miserably
[itex]2: \neg (\neg p \vee (q \vee r))[/itex] hypothesis
<start of hypothesis 1>
[itex]3: \neg p[/itex] hypothesis
[itex]4: \neg p \vee (q \vee r)[/itex] conjunction introduction 3
[itex]5: \bot[/itex] negation introduction 2,4
<end of hypothesis 1>
[itex]6: \neg \neg p[/itex] negation introduction 3-5
[itex]7: p[/itex] double negative elimination 6
[itex]8: ?[/itex]
<end of hypothesis 0>
As you can see, I don't exactly know how to use TeX.
PS: How do I put a box around the hypothesis in TeX?
Homework Statement
How to prove this
[itex](p \rightarrow (q \vee p)) \rightarrow r \vdash \neg p \vee (q \vee r)[/itex]
using only the natural deduction rules in propositional logic?
Homework Equations
http://en.wikipedia.org/wiki/Propositional_logic
(natural deduction rules only)
The Attempt at a Solution
[itex]1: (p \rightarrow (q \vee p)) \rightarrow r[/itex] premise
<start of hypothesis 0> ; I tried to make a box here but failed miserably
[itex]2: \neg (\neg p \vee (q \vee r))[/itex] hypothesis
<start of hypothesis 1>
[itex]3: \neg p[/itex] hypothesis
[itex]4: \neg p \vee (q \vee r)[/itex] conjunction introduction 3
[itex]5: \bot[/itex] negation introduction 2,4
<end of hypothesis 1>
[itex]6: \neg \neg p[/itex] negation introduction 3-5
[itex]7: p[/itex] double negative elimination 6
[itex]8: ?[/itex]
<end of hypothesis 0>
As you can see, I don't exactly know how to use TeX.
PS: How do I put a box around the hypothesis in TeX?
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