Math...not sure if I did this correctly.....please help!!

[jenzy569]

(a) translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.

If Nicholas Thompson teaches this course, then I will get a passing grade.

I did not get a passing grade.

? Nicholas Thompson did not teach the course.

I got:

Assume that p = Nicholas Thompson teaches this course. Assume q = I will get a passing grade. The symbolic form is ~q->~p

The truth table is:

p. ~p q. ~q. ~q->~p

T. F T. F. T
T. F F. T. F
F. T T. F. T
F. T F. T. T

So the conclusion is valid.

I don't believe this is correct....please help!

 

[soroban]

Re: Math...not sure if I did this correctly.....please help!

Hello, jenzy569!

(a) Translate the argument into symbolic form.
(b) Determine if the argument is valid or invalid.
You may compare the argument to a standard form or use a truth table.

If Nicholas Thompson teaches this course, then I will get a passing grade.
I did not get a passing grade.
? Nicholas Thompson did not teach the course.


\(\displaystyle \text{I got:}\)

\(\displaystyle p = \text{Nicholas Thompson teaches this course.}\)
\(\displaystyle q = \text{I will get a passing grade.}\)
\(\displaystyle \text{The symbolic form is: }\sim q \to \sim p\) . This is wrong.

The truth table is:

. . \(\displaystyle \begin{array}{|c|c|c|c||c|} \hline p & \sim\!p & q & \sim\!q & \sim\!q \to\, \sim\!p \\ \hline \\[-4mm] T&F&T&F&T \\ T&F&F&T&F \\ F&T&T&F&T \\ F&T&F&T&T \\ \hline \end{array}\) . This is wrong.

So the conclusion is valid. . This is wrong.

I don't believe this is correct. . You're right!

\(\displaystyle \text{The argument has this form: }\;\begin{array}{c} p \to q \\ \sim\!q \\ \hline \therefore \;\sim\!p\;\;\; \end{array}\)

\(\displaystyle \text{Hence, we have: }\:[(p \to q)\, \wedge \sim\!q] \to \,\sim\!p\)


\(\displaystyle \text{The truth table is:}\)

. . \(\displaystyle \begin{array}{|c|c||ccccccc|} \hline \\[-4mm] p & q & [(p & \to & q) & \wedge & \sim\!q] & \to & \sim\!p \\ \hline \\[-4mm] T&T&T&T&T&F&F&\bf{T}&F \\ T&F&T&F&F&T&T&\bf{T}&F \\ F&T&F&T&T&F&F&\bf{T}&T \\ F&F&F&T&F&T&T&\bf{T}&T \\ \hline && _1 & _2 & _1 & _3 & _1 & _4 & _1 \\ \hline \end{array}\)
. . . . . . . . . . . . . . . . . . . . . . . . . . \(\displaystyle \uparrow\)
. . . . . . . . . . . . . . . . . . . . . . . . .\(\displaystyle \text{Valid!}\)