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.
a) (p IMPLIES q) OR (p IMPLIES NOT q)
ReplyDelete1.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.