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

Algebra.Com
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)   (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)   (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/

RELATED QUESTIONS

Prove directly, no Conditional Proof or Indirect Proof 1. M ⊃ ~ C 2. ~C ⊃ ~ A (answered by math_tutor2020)
Prove directly, no Conditional Proof or Indirect Proof 1. I ∨ (N • F) 2. I ⊃ F (answered by math_tutor2020)
Using an ordinary proof (not a conditional or indirect proof) (answered by richwmiller)
Can i please have help solving these proofs? Use an ordinary proof (not conditional or... (answered by jim_thompson5910)
INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. (answered by AnlytcPhil)
INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. (answered by jim_thompson5910)
Using an ordinary proof (not a conditional or indirect proof) 1. S ⊃ (K ⋅... (answered by richwmiller)
i need help solving this indirect proof 1. (R v S) > (H & ~G) 2. (K v R) > (G v ~H) (answered by Edwin McCravy)
Use natural deduction to derive the conclusion of the following arguments. Do not use... (answered by math_helper)