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So here is my problem, I am asked to prove that P $\leftrightarrow$ (Q $\leftrightarrow$ R) is equal to (P $\leftrightarrow$ Q) $\leftrightarrow$ R, pretty straight forward. So I made this truth table to prove it, and the truth values match up perfectly so this proves that they are true. Here is the truth table.

Image of the truth table

I know the truth table is accurate , but how can I turn this into a proof? They usually start with assume P is true etc.. but I legitmately need an example of transforming this table into that.

fsdff
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  • To show two statements A and B are equal, you can (additinally) show A iff B is a tautology, i.e. Construct a final column [P iff (Q iff R)] iff [(P iff Q) iff R] and all the values must be T. This shows that regardless of the individual outcomes, the overall outcome will always be the same. – Inazuma Jan 17 '18 at 00:40
  • Are you expected to give a formal proof using a specific set of inference rules? Or is this to be proven informally? In the latter case, showing that their truth tables are identical suffices. – Justin Benfield Jan 17 '18 at 02:42
  • Yeah he wants a formal proof.. as in like words. I just don't get how to do it... Like I understand the truth table. – fsdff Jan 17 '18 at 03:38

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