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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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))
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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