Please help meeeee !!!!!! Logic !

[nannygee12]

given :
p ----> q
~q



Which is a logical solution ?

1. p
2. ~p
3. q
4. ~p^q

 

[DrPhil]

given :
p ----> q
~q

If ever p is true, then q is also true.
BUT, q is not true.
What can you say about p?

 

[JeffM]

given :
p ----> q
~q



Which is a logical solution ?

1. p
2. ~p
3. q
4. ~p^q

Sometimes it helps to substitute concrete examples for the abstract generalization.

Let p = "Tom is a puppy"

Let q = "Tom is a dog."

So it is certainly true to say "If Tom is a puppy, then Tom is a dog." So p implies q.

But if it is true that Tom is not a dog (say he is a cat), then what can you say about the truth or falsity of the statement that Tom is a puppy.

So ~q implies what?

 

[soroban]

Hello, nannygee12!

\(\displaystyle \text{Given: }\:\begin{array}{c}p \to q \\ \sim q\qquad \\ \hline \end{array}\)

\(\displaystyle \text{Which is a logical conclusion?}\)

. . \(\displaystyle 1.\;p \qquad 2.\;\sim p \qquad 3.\;q \qquad 4.\;\sim p \wedge q\)

Were you given any "rules" to work with?


\(\displaystyle \begin{array}{c}p\to q \\ \sim q\quad \\ \hline \end{array}\qquad\quad\text{Given}\)


\(\displaystyle \begin{array}{c} \sim q\to\:\sim p \\ \sim q\qquad \\ \hline \end{array}\quad\text{Contrapositive}\)


\(\displaystyle \begin{array}\sim q\to\sim p \\ \sim q\qquad \\ \hline \color{blue}{\sim p}\qquad \end{array}\quad\text{Detachment}\)