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Construct direct proofs to show that the following symbolic arguments are valid. Commas mark the breaks between premises. 1. F>(G→H), ~F→J, ~(G→H) .: J 2. P>Q, R→"S, P v R, (Q v ~S)-(~T v ~W), ~~T .: ~W 3. (A v G)→K, K→(B→F), A-B .. F

Construct direct proofs to show that the following symbolic arguments are valid. Commas mark the breaks between premises. 1. F>(G→H), ~F→J, ~(G→H) .: J 2. P>Q, R→"S, P v R, (Q v ~S)-(~T v ~W), ~~T .: ~W 3. (A v G)→K, K→(B→F), A-B .. F

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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therefore or ". :" (colon and period, in either order) arrow (dash + greater than), or simply ">' (less than + dash + greater than), or simply double arrow conjunction (dot) (a period) disjunction V (wedge) "v" (lower case letter vee) Construct direct proofs to show that the following symbolic arguments are valid. Commas mark the breaks between premises. 1. F>(G>H), ~F→J, ~(G→H) .. J 2. P>Q, R→"S, P v R, (Q v "S)-(~T v ^W), w~T ~W 3. (A v G)→K, K→(B→F), A·B F 4. "C→(F>C), ~C :. ~F 5. "(C·D), ~C→S, ~D→T :: S v T 6. (W->U).~X :. "U→~W 7. T v "R, "(S v ~R), (T.~S)→~Q,W>Q :: ~W 8. "(J-L), (~J v ~L)¬~M, ~E v (M v ~S) .: ~(S · E) 9. (BVA)→C, ~B→D, ~D .. C 10. "(0-N), (~O→S)·(~N→T) .: S v T 11. "M v N.. ~N→~M 12. "B&C, "B :: С 13. (Z v *Y)-(Z v W), Z→~U, ~Y>(W>U) .: U 14. "U→"B, S→~B, ~(U-~S), T v B .: T 15. A€В, В-Ус: ~AvC Use Conditional Proofs (CP) to show that each of the following symbolic arguments are valid. Commas mark the breaks between premises. 16. P→(Q→R) .: Q→(P→R) 17. P→Q :: P>(Q v R) 18. (B-D)→(C-R), D .. B¬R 19. (Z-"W)>(X-U), Z>(W>Y) .: Z–(^Y-¬U)
Transcribed Image Text:therefore or ". :" (colon and period, in either order) arrow (dash + greater than), or simply ">' (less than + dash + greater than), or simply double arrow conjunction (dot) (a period) disjunction V (wedge) "v" (lower case letter vee) Construct direct proofs to show that the following symbolic arguments are valid. Commas mark the breaks between premises. 1. F>(G>H), ~F→J, ~(G→H) .. J 2. P>Q, R→"S, P v R, (Q v "S)-(~T v ^W), w~T ~W 3. (A v G)→K, K→(B→F), A·B F 4. "C→(F>C), ~C :. ~F 5. "(C·D), ~C→S, ~D→T :: S v T 6. (W->U).~X :. "U→~W 7. T v "R, "(S v ~R), (T.~S)→~Q,W>Q :: ~W 8. "(J-L), (~J v ~L)¬~M, ~E v (M v ~S) .: ~(S · E) 9. (BVA)→C, ~B→D, ~D .. C 10. "(0-N), (~O→S)·(~N→T) .: S v T 11. "M v N.. ~N→~M 12. "B&C, "B :: С 13. (Z v *Y)-(Z v W), Z→~U, ~Y>(W>U) .: U 14. "U→"B, S→~B, ~(U-~S), T v B .: T 15. A€В, В-Ус: ~AvC Use Conditional Proofs (CP) to show that each of the following symbolic arguments are valid. Commas mark the breaks between premises. 16. P→(Q→R) .: Q→(P→R) 17. P→Q :: P>(Q v R) 18. (B-D)→(C-R), D .. B¬R 19. (Z-"W)>(X-U), Z>(W>Y) .: Z–(^Y-¬U)
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