# Thread: Need help with Logic :(

1. ## Need help with Logic :(

--------------------------------------------------------------------------------

I'm new here, not sure if this is the right forum to be but I'm really struggling in my logic class. I got a take home test and I really need help. If I don't pass this class, my GPA is going to go down, I lose about \$600, and I have to take the class over again. I have three weeks left and I'm only at about 61% right now. I really need all the help I can get.

Does anyone know anything about transitions and proofs?

These are the transitions:

It's false that both SMITH and JONES will teach summer school. If Smith teaches summer school, then the department secretary won't get GRUMPY, Consquently Jones won't teach summer school and the secretary won't get GRUMPY, since Smith will teach summer school.

This are the proofs I need help with:

P>Q, -Q&(S>T), P v R, R> S, }T

A v B, -B, A<>c, } C&-B

(K&M) > H, -H, (K & M) v (Q & H) } Q & M

With > (arrow)
<> (double arrow)
} is conclusion

Thanks :flowers:

2. Hello, LittleKat123!

I'm not sure what rules you are allowed to use.

You should be familiar with certain logic theorems.

. . $(p \rightarrow q) \land p \;\Rightarrow \;q$

. . $(p \rightarrow q)\, \land \sim\! q\;\Rightarrow\;\sim\!p$

. . $(p \lor q)\, \land \sim\! p\;\Rightarrow\;q$

I'll run through the first one . . .
You decide if any of this is useful to you.

$\begin{array}{ccccc}(1)\\(2)\\(3)\\(4)\\(5)\end{ar ray}\begin{array}{ccccc}P \rightarrow Q \\ \sim\!Q \land (S \rightarrow T) \\ P \lor R \\ R \rightarrow S \\ \therefore T \end{array}$

From (1) and (2): . $(P \rightarrow Q)\,\land \sim\!Q\;\Rightarrow\;\sim\!P$ [6]

From (3) and (6): . $(P\,\lor R)\, \land \sim\!P\;\Rightarrow\;R$ [7]

From (4) and (7): . $(R \rightarrow S) \land R\;\Rightarrow\;S$ [8]

From (2) and (8): . $(S \rightarrow T) \land S\;\Rightarrow\;T$

3. the conclusion is T, so I don't think that should be in the problem as an assumption. We are working with the following Derived rules:

Modus Tollens, Disjunctive Argument, Conjuctive Argument, Double Negation, DeMorgans Law, Arrow, and Contraposition

What is the ~ for? I'm just a bit confused, sorry.

4. Originally Posted by LittleKat123
the conclusion is T, so I don't think that should be in the problem as an assumption.

T is not "in" the problem.
It showed up in the final statement as a conclusion.

We are working with the following Derived rules:
Modus Tollens, Disjunctive Argument, Conjuctive Argument, Double Negation,
DeMorgans Law, Arrow, and Contraposition

You should be able to re-name the theorems I used.

What is the ~ for?

Since you can't guess what it is, it is the negation.
You probably prefer $\neg P$, right?

5. thank you