Premises: Vx(P(x) v Q(x)) \x((~P(x)^Q(x))→R(x)) Step 1. Vx(P(x) VQ(x)) 2. P(a) v Q(a) 3. P(a) v Q(a) v R (a) 4. \x((→P(x)^Q(x))→ R(x)) 5. (¬P(a)^Q(a))→R(a) 6. (P(a)^Q(a)) v R(a) 7. P(a)v-Q(a) v R (a) 8. P(a)✓ R(a) 9. (-R(a)) v P(a) 10. -R(a) →→ P(a) 11. Vx(-R(x)→P(x)) Reason Premise Premise Conclusion: Vx(-R(x)→ P(x))
Premises: Vx(P(x) v Q(x)) \x((~P(x)^Q(x))→R(x)) Step 1. Vx(P(x) VQ(x)) 2. P(a) v Q(a) 3. P(a) v Q(a) v R (a) 4. \x((→P(x)^Q(x))→ R(x)) 5. (¬P(a)^Q(a))→R(a) 6. (P(a)^Q(a)) v R(a) 7. P(a)v-Q(a) v R (a) 8. P(a)✓ R(a) 9. (-R(a)) v P(a) 10. -R(a) →→ P(a) 11. Vx(-R(x)→P(x)) Reason Premise Premise Conclusion: Vx(-R(x)→ P(x))
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
In the following argument, give a justification for each step.
![Premises:
vx(P(x)v Q(x))
\x((¬P(x)^Q(x))→R(x))
Step
1. Vx(P(x)Q(x))
2. P(a) v Q(a)
3. P(a)vQ(a) v R(a)
4. Vx((-P(x)^Q(x))→ R(x))
5. (P(a)^Q(a)) →→ R(a)
6. (P(a)^Q(a)) v R (a)
7. P(a)v-Q(a) v R (a)
8. P(a) v R(a)
9. (R(a)) v P(a)
10. -R(a) →→P(a)
11. Vx(-R(x)→P(x))
Reason
Premise
Premise
Conclusion: Vx(-R(x)→P(x))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0058694e-01c1-4ca5-8fce-b9137a5384c6%2Fe92bcafc-bdbb-4bd2-a308-5e63a8bc2e33%2F3soygwk_processed.png&w=3840&q=75)
Transcribed Image Text:Premises:
vx(P(x)v Q(x))
\x((¬P(x)^Q(x))→R(x))
Step
1. Vx(P(x)Q(x))
2. P(a) v Q(a)
3. P(a)vQ(a) v R(a)
4. Vx((-P(x)^Q(x))→ R(x))
5. (P(a)^Q(a)) →→ R(a)
6. (P(a)^Q(a)) v R (a)
7. P(a)v-Q(a) v R (a)
8. P(a) v R(a)
9. (R(a)) v P(a)
10. -R(a) →→P(a)
11. Vx(-R(x)→P(x))
Reason
Premise
Premise
Conclusion: Vx(-R(x)→P(x))
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