1. ## Truth Tables

Need help in completing this truth table.

P | Q | R | S | ~S | P^Q | R^S(the arrow goes down. cant find a down arrow)

2. Originally Posted by Siobhan
Need help in completing this truth table.

P | Q | R | S | NS | P^Q | R^S(the arrow goes down. cant find a down arrow)
What is the conclusion?

R wedge S ?

And, by NS, did you mean $\displaystyle {N}\cdot{S}$ ?

3. I really don't know if I have the correct wording on this. Please bare with me.

For example.

P Q 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

Please try to encode what I've typed in the above post. If you know these it would be a great help.

Thank you for understanding,
Siobhan

4. Originally Posted by Siobhan
I really don't know if I have the correct wording on this. Please bare with me.

For example.

P Q 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

Please try to encode what I've typed in the above post. If you know these it would be a great help.

Thank you for understanding,
Siobhan
I'm not the best with matrices in latex, but I'll try to help.

You've got the basic Idea. The number of lines needed will be 2 raised to the number of simple statements. Or

$\displaystyle L=2^n$

So you will need $\displaystyle 2^5=32$ lines if N is a simple statement, but I think by N, you may be trying to say "not"S, or $\displaystyle \sim{S}$. Is this correct. If so you will only need 16 lines.

5. Updated. The N was a ~ LOL. My messy writing. Still need help with this though.

6. Originally Posted by Siobhan
Updated. The N was a ~ LOL. My messy writing. Still need help with this though.
Okay then...

I assume that this is an argument with $\displaystyle R\vee{S}$ the conclusion. Is this correct?

7. Yup, correct

8. Originally Posted by Siobhan
Yup, correct
Dude, I can't get the LaTex right, but

There will be 8 Ts and them 8 Fs under the P. Then The Ts and Fs will alternate by fours for the Qs. Then the Ts and Fs will alternate by 2s for the Rs, and by 1 for the Ss.

After you have written the 16 lines, change the truth values for the tildes. Then understand that a wedge is only false when both of its disjuncts are false. Then, look for a line in which all of the premises are true, but the conclusion is false, if this does not happen, the argument is valid.

Im sorry if this is vague. I will compute the truth table and get right back to you with the answer. Thanks for being patient with me.

9. argument appears to be valid.