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I Show [ (A -> B) ^ (B -> C) ] -> (A -> C)

  1. Jan 25, 2017 #1
    Hello,

    I need to show that the following is a tautology using only logical equivalences. I am not allowed to use hypothetical syllogism or other rules of inference.

    [ (A -> B) ^ (B -> C) ] -> (A -> C)

    I've been trying this for hours, and I haven't been able to do this without resorting to a truth table, a truth tree, or rules of inference. Is there actually a way to show that this is a tautology by using the rules below?

    upload_2017-1-25_12-21-3.png

    upload_2017-1-25_12-21-26.png
     
  2. jcsd
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