# Math Help - Valid or Invalid Arguments

1. ## Valid or Invalid Arguments

Very confused about valid or invalid arguments and knowing when and when not to construct truth tables or when to use the standard form for example:
I understand how to construct tables for example for p, q, r. Confused on how to present the argument.

Problem:
p v q
~q
therefore P

Assistance is greatly appreciated and needed.

gperson

2. When determining the validity of this argument, you can use a truth table. But you can also use an explanation of it to a certain extent to where the validity of the argument is stated or implied.

We have p or q. And we have to assume not q and therefore get p.

1. p v q hyp
2. ~q hyp
3. p 1, 2, disjunctive syllogism

Roughly speaking, using the or connective, we are told that at least one of the statements is true, and then we are told that q is not true, so we can infer that the p must be true.

3. Hello, gperson!

p v q
. ~q
-----
. p

The argument is: . $\bigg[(p \vee q) \:\wedge \sim q\bigg] \;\to \;\;\sim q$

The truth table looks like this:

. . $\begin{array}{|c|c|ccccccc}
p & q & [(p & \vee & q) & \wedge & \sim q] & \to & p \\ \hline
T & T & T & T & T & F & F & {\color{blue}T} & T \\
T & F & T & T & F & T & T & {\color{blue}T} & T \\
F & T & F & T & T & F & F & {\color{blue}T} & F \\
F & F & F & F & F & F & T & {\color{blue}T} & F \\ \hline
& & _1 & _2 & _1 & _3 & _1 & _4 & _1
\end{array}$

4. ## Arguments & Truth Tables

Thanks Aryth as this is very helpful. I am still learning how to use the various arguments and it can get quite confusing. Your help is greatly appreciated and needed. Your directions were easier to understand than many web sites I visited for clarity. Clear directions make a difference.

I have other types of arguments that I am trying to work on and it is confusing to me.

Again, I really appreicate your assistance

gperson