@jumico,

jumico;62921 wrote:I'm sure you get tired of people asking for help with study problems but I'd appreciate the help.

I can use the 19 rules of inference.

Where the spaces are theres supposed to be the if then sign. It doesn't show up on my screen.

Basically I'm supposed to prove a few problems like this. This is one.

If P then R

Therefore (If P and Q) then R

I'm really confused and I can't seem to make any progress.

Is simplification only okay when an and statement is by itself?

So you couldn't say "If P then "R and Q" and the just put down a Q or R as a simplification. I think that made sense.

Dear Jumico:

First, you must understand the rule. The premise says if P then R... Therefore, whenever you have P then R should follow... Many logical fallacies are committed because we tend to ADD crucial operative words that change the meaning of premises drastically. For instance, some people tend to read the premise as If ONLY P then R, which is obviously different.

So, whenever you have P (whether alone or with conjunction of others) you must have R.

If P then R

Therefore if P and Q then R

Note that the above argument may be expressed as follows:

If P then R

It is P and Q

Therefore it is R

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

This said, here is the proof:

If P and Q

Then it is P*

Now replace the conclusion above (It is P) in the original argument with (If P and Q):

If P then R

It is P

Therefore it is R

* Of course it is also: "Then it is Q". But this is not relevant for this proof.

I hope this helps

Peace,

Edip