Are (A then B) then C and (A and B) then C equivalent?

[Gamecockgirl]

I need help proving that (A then B) then C and (A and B) then C are equivalent. Can anyone help?

 

[Evo]

This doesn't meet criterai for posting in Philosophy. If this is homework, please post in the appropriate Homework forum

 

[HallsofIvy]

I am moving this to the "precalculus homework" forum.

Gamecock Girl, I think the simplest way to do this is to use a "truth table". There are 2³ different ways A, B, and C can be "True" or "False". The two statements are equivalent if they are both True or both False in each of those.

Writing "T" for True, "F" for False and "ABC" in that order, the 8 ways are:
TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF. Assuming you know what "if (if A then B) then C" and "if (A and B) then C" mean, you can decide whether they are True of False in each of those 8 situations.