# Is this argument valid?

• Oct 1st 2009, 07:57 PM
GreenDay14
Is this argument valid?
I have to find out whether this argument is valid or invalid:

p -> q
(q v ([not]r)) -> (p [and] s)
s->(r v q)

Hope that makes sense, and also I appreciate any help that can be offered. Thanks.
• Oct 4th 2009, 07:41 AM
Jones
Quote:

Originally Posted by GreenDay14
I have to find out whether this argument is valid or invalid:

p -> q
(q v ([not]r)) -> (p [and] s)
s->(r v q)

Hope that makes sense, and also I appreciate any help that can be offered. Thanks.

If im not mistaken it's valid.

You can check for yourself, if you find values for s,r,p and q that makes the result false but the statements true, then the argument is invalid
• Oct 4th 2009, 08:22 AM
Hello GreenDay14
Quote:

Originally Posted by GreenDay14
I have to find out whether this argument is valid or invalid:

p -> q
(q v ([not]r)) -> (p [and] s)
s->(r v q)

Hope that makes sense, and also I appreciate any help that can be offered. Thanks.

I've drawn up a truth table for the proposition

$((p \rightarrow q)\land((q\lor \neg r)\rightarrow(p\land s)))\rightarrow(s\rightarrow (r\lor q))$

- see attachment.

The columns are evaluated in order (1) through (8) - (8) being the final output. Since this show TRUE in every row, then, yes the argument is valid.