SOLUTION: Prove directly - NO Conditional Proof or Indirect Proof. 1. R ⊃ A / R ⊃ ( A v W )

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Question 1193810: Prove directly - NO Conditional Proof or Indirect Proof.
1. R ⊃ A / R ⊃ ( A v W )
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

    1.  R ⊃ A   / R ⊃ (A v W)

    2.  R ⊃ (A v W)    1,addition

[Replacing A by A v W,  sometimes called "disjunction introduction"]

https://www.youtube.com/watch?v=IN9nUurGpsk
https://en.wikipedia.org/wiki/Disjunction_introduction



Edwin

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Another approach:
NumberStatementLine(s) UsedReason
1R ⊃ A
:.R ⊃ (A v W)
2~R v A1Material Implication
3(~R v A) v W2Addition
4~R v (A v W)3Association
5R ⊃ (A v W)4Material Implication

For more information, check out the various rules of inference and rules of replacement as shown in the link below.
https://logiccurriculum.com/2019/02/09/rules-for-proofs/