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PostPosted: Wed, 6 Oct 2010 10:56:25 UTC 
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Use propositional logic to prove that the statement is valid:

1) [A → (B → C)] ^ (A V ~D) ^ B → (D → C)
2) (A → B) ^ [B → (C → D)] ^ [A → (B → C)] → (A → D)
3) A V B, A → C, B → C → C

Hope to get some help by getting some sort of step-to-step instructions.

Thanks!


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PostPosted: Wed, 6 Oct 2010 16:57:46 UTC 
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
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Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
cvkz wrote:
Use propositional logic to prove that the statement is valid:

1) [A → (B → C)] ^ (A V ~D) ^ B → (D → C)
2) (A → B) ^ [B → (C → D)] ^ [A → (B → C)] → (A → D)
3) A V B, A → C, B → C → C

Hope to get some help by getting some sort of step-to-step instructions.

Thanks!


First, you need a lot more brackets/parentheses.

How much propositional logic do you know? In particular, if you know the soundness and completeness theorem of first order propositional calculus then you can do with a truth table. If not, are you allowed to use derived argument form or just modus ponen?

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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