How to Prove A v C in Symbolic Logic?

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In summary, symbolic logic is a formal system of reasoning that uses symbols and rules to represent and evaluate logical arguments and mathematical concepts. It differs from traditional logic by using mathematical notation instead of natural language, allowing for a more precise analysis. It is important because it is widely used in various fields and provides a systematic approach to logical analysis. Common symbols used in symbolic logic include logical operators and quantifiers. To improve understanding, practice using symbolic notation and work through examples and exercises.
  • #1
questiongirl111
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The question asks you to prove A v C

This is what I have. Everything is correct until the last question, #11

1. A V C
2. ~BvC
3.(new subproof) B
4. (new subproof ~B
5. contradiction contradiction intro 4,3
(end subproof from 4-5)
6. ~BvC V Intro 2
(end subproof from 3-6)
7. (new subproof) A
8. A v B vINTRO 1
(end subproof from 7-8)

9.(new subproof) C
10. ~BvC (vINTRO 2)
(end subproof 9-10)
11.A v C VINTRO ?


Thanks!
-J
 
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  • #2
What class is this for? What does vINTRO mean?
 
  • #3
ohn

Hello John,

In order to prove A v C, you need to show that either A or C is true. In your proof, you have already shown that ~B v C is true (lines 2 and 6). Now, you just need to show that either A or C is true.

In line 7, you have started a subproof to show that A is true. You can continue this subproof by showing that A v C is true (line 8). Similarly, in line 9, you have started a subproof to show that C is true. You can continue this subproof by showing that A v C is true (line 10).

Therefore, using the v Intro rule, you can conclude that A v C is true (line 11) since you have shown that either A or C is true in both subproofs.

I hope this helps! Let me know if you have any further questions. Good luck with your symbolic logic work.

Best,
 

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