Question 1201697
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Refer to rules 4, 5, 7, and 9.
*[illustration Screenshot_139.png]
Image Source:
<a href = "https://logiccurriculum.com/2019/02/09/rules-for-proofs/">https://logiccurriculum.com/2019/02/09/rules-for-proofs/</a>
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
<a href = "https://www.tutorialspoint.com/discrete_mathematics/rules_of_inference.htm">https://www.tutorialspoint.com/discrete_mathematics/rules_of_inference.htm</a>
<a href = "https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/2%3A_Logic/2.6_Arguments_and_Rules_of_Inference">https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/2%3A_Logic/2.6_Arguments_and_Rules_of_Inference</a>
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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