Question 380486
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Let *[tex \Large p] represent the statement: "Ed is guilty"


Then *[tex \Large \neg p] must represent the statement: "Ed is not guilty"


Let *[tex \Large q] represent the statement: "Jack is telling the truth"


Then *[tex \Large \neg q] represents the statement: "Jack is not telling the truth."


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \neg p\ \rightarrow\ q]


represents the conditional given, namely "If Ed is not guilty, then Jack is telling the truth."


Since the contrapositive of a conditional statement always has the same truth value as the conditional statement, that is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (P\ \rightarrow\ Q)\ \leftrightarrow\ (\neg Q\ \rightarrow\ \neg P)]


And we can form the contrapositive of


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \neg p\ \rightarrow\ q]


beginning with the other given, namely *[tex \Large \neg q] by saying:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \neg q\ \rightarrow\ p]


And it is correct to conclude that Ed is guilty.


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