4. For each equivalence below, either provide a derivation from one side of the equivalence to the other (justify each step of your derivation with a brief explanation for example, by naming one of the equivalences, or show that the equivalence does not hold (warning: you cannot use a derivation to show non-equivalence- instead, think carefully about what an equivalence means, and how you can disprove it). (a) (b) 5. (4 -QV (PA-Q) ((PVQ) ⇒R) (¬PVQ) A-Q (P⇒ (QVR)) Use a truth table to prove that (PQ) ((PAQ) V (PA¬Q)).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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4. For each equivalence below, either provide a derivation from one side of the equivalence to the other
(justify each step of your derivation with a brief explanation for example, by naming one of the
equivalences, or show that the equivalence does not hold (warning: you cannot use a derivation to
show non-equivalence instead, think carefully about what an equivalence means, and how you can
disprove it).
(a)
(b)
5. (4
¬QV (PA-Q)
((PVQ)
(-PVQ) A-Q
R)
(P
(QVR))
Use a truth table to prove that (PQ) ((PAQ) V (¬PA¬Q)).
Transcribed Image Text:4. For each equivalence below, either provide a derivation from one side of the equivalence to the other (justify each step of your derivation with a brief explanation for example, by naming one of the equivalences, or show that the equivalence does not hold (warning: you cannot use a derivation to show non-equivalence instead, think carefully about what an equivalence means, and how you can disprove it). (a) (b) 5. (4 ¬QV (PA-Q) ((PVQ) (-PVQ) A-Q R) (P (QVR)) Use a truth table to prove that (PQ) ((PAQ) V (¬PA¬Q)).
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