54. (p^ (~(~p V 9))) V (p ^ q) =p

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.5: The Format Proof Of A Theorem
Problem 11E: When can a theorem be cited as a reason reason in a proof?
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Question 54

Use Theorem 2.1.1 to verify the logical equivalences in
50-54. Supply a reason for each step.
50. (р^~д) Vр—р
51. p^(~qv p) = p
52. ~(p v ~q) v (~p^~q) = ~p
53. ~((~p ^q) V(~p^~q)) V (p ^q) = p
54. (р^(~(~рV))V (р^ф) —р
Transcribed Image Text:Use Theorem 2.1.1 to verify the logical equivalences in 50-54. Supply a reason for each step. 50. (р^~д) Vр—р 51. p^(~qv p) = p 52. ~(p v ~q) v (~p^~q) = ~p 53. ~((~p ^q) V(~p^~q)) V (p ^q) = p 54. (р^(~(~рV))V (р^ф) —р
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