# Thread: Help with a few propositional logic proofs

1. ## Help with a few propositional logic proofs

I'm having a really hard time solving the following proofs in Tomassi's Logic book.

1)
P v Q : (P v R) -> (P v(Q & R))

2)
P : Q -> (P <->Q)

3)

P v (Q v R) : Q v (P v R)

2. Originally Posted by unprocessed9
I'm having a really hard time solving the following proofs in Tomassi's Logic book.
1) P v Q : (P v R) -> (P v(Q & R))
Please explain what the notation means and what are you to do with it.

3. I have to prove the proofs using steps and specific notations (used in the Tomassi Book)

4. Originally Posted by unprocessed9
(used in the Tomassi Book)
I for one have never heard of Tomassi much less his textbook (I taught logic many times).
It would be shear accident if anyone here knows the notation used in a particular text.
So if you want help with this, you are going have to type out the list of rules and notations used in that text.

5. Originally Posted by Plato
I for one have never heard of Tomassi much less his textbook (I taught logic many times).
It would be shear accident if anyone here knows the notation used in a particular text.
So if you want help with this, you are going have to type out the list of rules and notations used in that text.
& And
&I And Introduction

v Or
(vE) Or Elimination
(vI) Or Introductioni

-> If…then
->I
->E

<-> If and only if

~ Not

There are also rules of assuming for the antecedent of a conditional (assumption cp), and assumption for part of an 'or' statement (assumption vE)

6. Originally Posted by unprocessed9
I'm having a really hard time solving the following proofs in Tomassi's Logic book.

1)
P v Q : (P v R) -> (P v(Q & R))

2)
P : Q -> (P <->Q)

3)

P v (Q v R) : Q v (P v R)
Assuming that : means equivalent then No 3 can be solved in the following way:

P v (Q v R) = (P v Q)v R =.................................. ( by associativity)

=(Q v P)v R = .................................................. ..(By commutativity)

=Q v (P v R) .................................................. ......(BY associativity again).

Do you want the rest of the problems solved in this way??