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) -QV (PA-Q) (-PVQ) A-Q (b). ((PVQ) ⇒R) (P➡ (QVR))

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) -QV (PA-Q) (-PVQ) A-Q (b). ((PVQ) ⇒R) (P➡ (QVR))

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 15E: Let A=R0, the set of all nonzero real numbers, and consider the following relations on AA. Decide in...

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