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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## 1 comment:

a) (

pIMPLIESq) OR (pIMPLIES NOTq)1.

p________________ T T F F2.

q________________ T F T F3.NOT

q____________ F T F T4.

pIMPLIESq______ T F T T5.

pIMPLIES NOTq__ F T T Tline 4 OR line 5___ T T T T

It's a tautology.

b) (NOT

p) IMPLIES (pIMPLIESq)1.

p____________________ T T F F2.

q____________________ T F T F3.NOT

p________________ F F T T4.

pIMPLIESq__________ T F T T5.line 3 IMPLIES line 4__ T T T T

Again, it's a tautology.

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