Kaye ex. 4.2, p 40 (0) Comment a < b (1) Given b < c (2) Given a < c (3) Transitivity (1) (2) c < a (4) Given a < a (5) Transitivity (3) (4) F (6) Irreflexivity (5) True Kaye ex. 4.3, p. 40 (0) Comment a < b (1) Given b < c (2) Given a < c (3) Transitivity (1) (2) |c < a (4) Assumption |a < a (5) Transitivity (3) (4) |F (6) Irreflexivity (5) c /< a (7) Reductio Ad Absurdum (4) (6) True Kaye ex. 4.4, p. 41 (0) Comment a < b (1) Given |b < a (2) Assumption |a < a (3) Transitivity (1) (2) |F (4) Irreflexivity (3) b /< a (5) Reductio Ad Absurdum (2) (4) True Kaye ex. 4.6, p. 41 (0) Comment c < b (1) Given a /< b (2) Given |a < c (3) Assumption |a < b (4) Transitivity (3) (1) |F (5) Contradiction (4) (2) a /< c (6) Reductio Ad Absurdum (3) (5) True