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

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Question 1201697: 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 need help on is this a simplication proof example A v B
A
Found 2 solutions by mccravyedwin, math_tutor2020:
Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!
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.

================================================


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.

=======================================
 
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
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Refer to rules 4, 5, 7, and 9.

Image Source:
https://logiccurriculum.com/2019/02/09/rules-for-proofs/
That page goes over the various logic rules of inference and rules of replacement.
The screenshot shown above focuses on the rules of inference specifically.

We cannot use rule 9 (addition) in reverse.
We cannot go from "P v Q" to "P".
However, rule 5 (conjunction) does work in reverse (to get rule 7 simplification).

Further Reading
https://www.tutorialspoint.com/discrete_mathematics/rules_of_inference.htm
https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/2%3A_Logic/2.6_Arguments_and_Rules_of_Inference
The second link refers to "Elimination", which is really "Disjunctive Syllogism" by another name.
Also, that second link talks about "Transitivity" aka "Hypothetical Syllogism".
There are probably other examples of rules going by multiple names.

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