# Truth Table

• Jul 20th 2010, 06:01 PM
brumby_3
Truth Table
How do I construct the truth table for the following proposition: Yfrog Image : yfrog.com/59truthtablep

• Jul 20th 2010, 06:03 PM
Ackbeet
The same way you construct any truth table: one piece at a time. You only have two variables, which means you'll only need 4 rows. How did you start out?
• Jul 20th 2010, 06:11 PM
brumby_3
Okay so the first two columns consist of all combinations of p and q, ie TT, TF, FT and FF. Then does the next column have the heading q^p?
• Jul 20th 2010, 06:12 PM
Ackbeet
Looks like a good first step. What values do you get?
• Jul 20th 2010, 06:17 PM
brumby_3
To be honest I'm not sure how to figure the values out. This is what's confusing me. Here's a guess: T, F, F, T or maybe they're all T?
• Jul 20th 2010, 06:20 PM
Ackbeet
Neither, I'm afraid. The AND works like this: p^q is true only if both p is true, and q is true. If either or both are false, then the AND function gives you a false. So, with that information, what do you get?
• Jul 20th 2010, 06:30 PM
brumby_3
So it is T, F, F, F?
• Jul 20th 2010, 10:44 PM
integral
take (p and q)

For (p,q)
(1,1)--> 1
(1,0)--> 0
(0,1)--> 0
(0,0)--> 0

Think about it now.
• Jul 21st 2010, 01:55 AM
Ackbeet
That's correct. What step should you take now?
• Jul 21st 2010, 09:59 AM
usagi_killer
This is how I'd do it.

Sorry I don't know how to do tables in LaTeX so I did it in paint, hope it's alright. I attached the file.

Note the last 2 rows, they are vacuously true since p is F.

Hope that helps... if you can any problems feel free to ask and I'll try explain.