SOLUTION: Is the rule of conjunction like this example true? P v Q Q v P (P v Q) · (Q v P) Is this example a disjunctive syllogism? P v Q ~Q__ ~P The last question I

Is the rule of conjunction like this example true? P v Q
Q v P
therefore (P v Q) · (Q v P)

Yes.

Here is what disjunctive syllogism is all about:

Yes, if both these are true

1. You have a cat  
2. You have a dog

then this is true:

3. You have a cat AND you have a dog.

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Is this example a disjunctive syllogism? 
P v Q
~Q__
~P

No it is not.  Take off the ~ on the ~P. Then this would be a case of
disjunctive syllogism.

P v Q
 ~Q 
P

Here is what disjunctive syllogism is all about:

If both the following are true:

1. You have a cat OR you have a dog.
2. You do not have a cat.

Then this is true:

3.  You have a dog.

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The last question I need help on is this a simplification proof example 

A v B
A

No, it is not. Replace the v by · and it would be.

This is simplification:

A ∙ B
A

Here is what simplification is all about:

If the following is true:

1.  You have a cat AND you have a dog

then this is true:

2.  You have a cat.

Edwin