Instead of columns running left to right, it's easier in this text editor to make a truth table that is put together in rows going from top to bottom
Here is an example: Create the truth table for (p OR q) IMPLIES q.
p__________________ T T F F
q__________________ T F T F
p OR q_____________ T T T F
(p OR q) IMPLIES q_ T F T T
Not a tautology, because of the F in the second position.
Try the following.
a) (p IMPLIES q) OR (p IMPLIES NOT q)
b) (NOT p) IMPLIES (p IMPLIES q)
Answers in the comments.
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a) (p IMPLIES q) OR (p IMPLIES NOT q)
1.p________________ T T F F
2.q________________ T F T F
3.NOT q____________ F T F T
4.p IMPLIES q______ T F T T
5.p IMPLIES NOT q__ F T T T
line 4 OR line 5___ T T T T
It's a tautology.
b) (NOT p) IMPLIES (p IMPLIES q)
1.p____________________ T T F F
2.q____________________ T F T F
3.NOT p________________ F F T T
4.p IMPLIES q__________ T F T T
5.line 3 IMPLIES line 4__ T T T T
Again, it's a tautology.
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