Question 633618
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1.\ R\ \small{\wedge}\LARGE\ S\ \ \ \ \ ] Premise


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2.\ S\ \rightarrow\ (P\ \rightarrow\ Q)\ \ ] Premise


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3.\ Q\ \rightarrow\ P\ \ ] Premise


Prove:  *[tex \LARGE \ \ \ P\ \leftrightarrow\ Q]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4.\  S\ \ \ \ \ \ \ \ \ :] From 1 by Conjunction Elimination


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5.\  P\ \rightarrow\ Q\ :] From 2 by Modus Ponens


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6.\  P\ \leftrightarrow\ Q\ :] From 3 and 5 by Biconditional Introduction


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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