Please do not use truth tables for anything.

Give a Hilbert proof to show the following: (p+q) + (q V (p = q)) Your Hilbert proof cannot use any shortcuts; i.e., it must be a Hilbert proof by Definition 1.4.5 in the book. (Hint: It might help to first write out a proof in a looser style and then fill in the shortcuts used later. Be careful not to skip steps; the shortest proof I found uses 12 lines). Give a Hilbert proof to show the following: (p+q) + (q V (p = q)) Your Hilbert proof cannot use any shortcuts; i.e., it must be a Hilbert proof by Definition 1.4.5 in the book. (Hint: It might help to first write out a proof in a looser style and then fill in the shortcuts used later. Be careful not to skip steps; the shortest proof I found uses 12 lines)