Question 760899
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		<td>*[tex \LARGE R\rightarrow S]</td>
		<td>To Show</td>
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		<td>1.</td>
		<td>*[tex \LARGE \neg(P\cdot\neg Q)]</td>
		<td>Premise</td>
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		<td>2.</td>
		<td>*[tex \LARGE \neg P\rightarrow\ \neg R]</td>
		<td>Premise</td>
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		<td>3.</td>
		<td>*[tex \LARGE (R\cdot Q)\rightarrow S]</td>
		<td>Premise</td>
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		<td>*[tex \LARGE \ \] 4.</td>
		<td>Suppose R</td>
		<td>Assumption</td>
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		<td>*[tex \LARGE \ \ ]5.</td>
		<td>*[tex \LARGE R\rightarrow P]</td>
		<td>2,4 Modus Tollens</td>
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		<td>*[tex \LARGE \ \]6. </td>
		<td>*[tex \LARGE \neg P v Q]</td>
		<td>1 DeMorgan</td>
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		<td>*[tex \LARGE \ \]7. </td>
		<td>*[tex \LARGE P\rightarrow Q]</td>
		<td>6 Equivalent</td>
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		<td>*[tex \LARGE \ \]8. </td>
		<td>*[tex \LARGE R\rightarrow Q]</td>
		<td>6,7 hypothetical syllogism</td>
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		<td>*[tex \LARGE \ \]9. </td>
		<td>*[tex \LARGE Q]</td>
		<td>4,8 Modus Ponens</td>
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		<td>*[tex \LARGE \ \]10. </td>
		<td> *[tex \LARGE R\cdot Q] </td>
		<td>4, 9 Conjunction</td>
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		<td>*[tex \LARGE \ \]12. </td>
		<td> *[tex \LARGE (R\cdot Q)\rightarrow S \vdash R\rightarrow S]</td>
		<td>Simplification</td>
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John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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