Can you prove these equations? (I did. The link to my solutions is here.)

Though it may seem to be a bit of a jump, the study of algorithms like these ones is actually closely related to the study of artificial intelligence. After all, if you strip down famous AIs like Watson or Cleverbot, all they really are are a lot of algorithms and if-else statements. Powerful algorithms allow these AIs to give the illusion of human-like intelligence by stringing together sentences and analyzing auditory input, among other things.

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