Answer to Question #180290 in Discrete Mathematics for jezelynfabeliniacorte

Question #180290

Construct a formal proof of validity for the following argument. [10]

1. (N v O) → P

2. (P v Q) → R

3. Q v N

4. ¬ Q

∴ R


1
Expert's answer
2021-04-13T14:13:53-0400

Let us construct a formal proof of validity from premises 1.- 4. to the conclusion "R" using rules of inference :


"1.\\ (N \\lor O) \u2192 P\\\\"

"2.\\ (P \\lor Q) \u2192 R\\\\"

"3.\\ Q \\lor N\\\\"

"4.\\ \u00ac Q"


"5.\\ N" (using Disjunctive Syllogism to the premises 3. and 4.)


"6.\\ N\\lor O" (using Disjunction Introduction to 5.)


"7.\\ P" (using Modus Ponens to 6. and 1.)


"8.\\ P\\lor Q" (using Disjunction Introduction to 7.)


"9.\\ R" (using Modus Ponens to 8. and 2.)




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Comments

Assignment Expert
12.06.21, 14:40

Dear John Rosfe G. Yuag, please use the panel for submitting a new question.


John Rosfe G. Yuag
20.05.21, 22:05

Construct a formal proof of the validity of the following argument. “The Chocolate hills are not chocolates if I’m not the president of the Philippines. I’m not the president of the Philippines. Therefore, the chocolate hills are chocolate.”

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