How do you construct a truth table for a compound statement?

Question

for example ~p or (q ^ ~r)

Answer 1

you have 3 variables so you got 4 columns x 8 rows.

Answer 2

Well, your compound statement would be true if p is false, or if q is true and r is false. So you need to set the table up with these 5 column headers:

~p
q
~r
q^~r
~p or (q ^ ~r)

Then you'd have 8 rows. Why 8? Because you have 2 possible values (T,F) for each of your 3 variables (p,q,r) ... so 2^3 = 8

In rows 1-4, ~p = T
In rows 5-8, ~p = F

In rows 1-2 and 5-6, q = T
In rows 3-4 and 7-8, q = T

In rows 1, 3, 5, and 7, ~r = T
In rows 2, 4, 6, and 8, ~r = F

I will leave it to you to determine what goes in the other two columns for each row. These problems are actually quite fun, and I wouldn't want you to miss out on doing part of your own problem yourself!

Good luck, and if you have further questions once you fill out your 4th and 5th columns, please come back and ask! Or send me an email!

Answer 3

You start off by listing all the possible combinations of True and False for p, q, and r:
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
You'll then create columns (one each) for ~p, ~r, q ^ ~ r, and your overall statement ~p V (q ^ ~r). To do each of those you need to know the rules for when and, or, and not are each true. You find the value for the two things that go into each statement and fill out the column accordingly.