Construct direct proofs to show that the following symbolic arguments are valid. Commas mark the breaks between premises. F→(G→H), ~F→J, ~(G→H) ∴ J P→Q , R→~S, P v R, (Q v ~S)→(~T v ~W), ~~T ∴ ~W (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. F→(G→H), ~F→J, ~(G→H) ∴ J P→Q , R→~S, P v R, (Q v ~S)→(~T v ~W), ~~T ∴ ~W (A v G)→K, K→(B→F), A∙B ∴ F
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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Construct direct proofs to show that the following symbolic arguments are valid. Commas mark the breaks between premises.
- F→(G→H), ~F→J, ~(G→H) ∴ J
- P→Q , R→~S, P v R, (Q v ~S)→(~T v ~W), ~~T ∴ ~W
- (A v G)→K, K→(B→F), A∙B ∴ F
- ~C→(F→C), ~C ∴ ~F
- ~(C∙D), ~C→S, ~D→T ∴ S v T
- (W→U)∙~X ∴ ~U→~W
- ~~T v ~R, ~(S v ~R), (T∙~S)→~Q , W→Q ∴ ~W
- ~(J∙L), (~J v ~L)→~M, ~E v (M v ~S) ∴ ~(S∙E)
- (B∨A)→C, ~B→D, ~D ∴ C
- ~(O∙N), (~O→S)∙(~N→T) ∴ S v T
- ~M v N ∴ ~N→~M
- ~B↔C, ~B ∴ C
- (Z v ~Y)∙(Z v W), Z→~~U, ~Y→(W→U) ∴ U
- ~U→~B, S→~B, ~(U∙~S), T v B ∴ T
- A↔B, B→C ∴ ~A v C
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