# Math Help - Rules of Inference

1. ## Rules of Inference

Establish the validity of the following:
p →¬q
¬q
p∨r
∴ ¬r
I am stuck with this problem. Can anyone give me some advice with this?

Thanks for the help!

2. Hello Gilvanildo
Originally Posted by Gilvanildo
Establish the validity of the following:
p →¬q
¬q
p∨r
∴ ¬r
I am stuck with this problem. Can anyone give me some advice with this?

Thanks for the help!
This argument is not valid. A counter-example is simply any proposition $p$ (true or false), $q$ false, and $r$ true. All of the first three statements are then true, but the conclusion is false.