Analyzing Arguments: Valid or Invalid?

[mr_coffee]

Hello everyone! its me!

I'm pretty sure I did these right but I need to make sure, the class average on the hws have been 70s, so i wonder what i got


Directions:
Some of the arguments in 7-18 are valid by universla modus ponens or universal modus tollens; others are invaldi and exhibit the converse or the inverse error State which are valid and which are invalid. Justify your answers.

#14.

If a complication of a computer porgram produces error messages, then the program is not correct.

Compliation of this program does not produce error messages.

.:. This program is correct.

I said P(x) = compliation of a computer program produces error messages
Q(x) = the program is not correct.

So,
$$\forall$$, if P(x) then Q(x)
~P(x)
.:. ~Q(x)


invalid, inverse error.


#17. If an infintie series converges, then its temrs go to 0.

The terms of the infinite series n/(n+1) do not go to 0.

.:. THe infine series n/(n+1) does not converge.

So i wrote:

$$\forall$$ x, if P(x) then Q(x)
~Q(x)
.:. ~P(x)

Valid, Universal modus Tollens.

Thanks!

 

[mighty2000]

Hello!

I can confirm that your reasoning for #14 is correct. It is an invalid argument as it exhibits the inverse error. The correct form of the argument should be:

If a complication of a computer program produces error messages, then the program is not correct.
The program is correct.
.:. Compilation of this program does not produce error messages.

In this case, the argument is valid as it follows the universal modus ponens form.

For #17, your reasoning is also correct. It is a valid argument as it follows the universal modus tollens form. The correct form of the argument should be:

If an infinite series converges, then its terms go to 0.
The terms of the infinite series n/(n+1) do not go to 0.
.:. The infinite series n/(n+1) does not converge.

Thank you for double checking your work and using logic to support your answers. Keep up the good work!