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)

Quote:

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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))

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Please explain what the notation means and what are you to do with it.

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

Quote:

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Originally Posted by unprocessed9

(used in the Tomassi Book)

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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.

Quote:

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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.

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& 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)

Quote:

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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)

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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??