(ii) ¬(p alternatively ¬p ¬q (1 mark)   q) (b) ¬p  ¬p q F T F F T T T T (2 marks 1 for each column). – 16. (a) (i) ¬q ¬p (1 mark)  (ii) (p (1 mark for q 1 mark (p r) for WITH parentheses)   and  q r) (b) If Alex does not play the flute then it is not true that he is a scientist or from Uruguay. OR If Alex does not play the flute then he is neither a scientist nor from Uruguay. (1 mark for 1 mark for antecedent, 1 mark for consequent) ‘if…then…, (c) ¬(q ¬r ¬(q     q p p) p) T F T T F F T F T T F F T F T T F F F T T F T T (1 mark for each correct column total of 3 marks) – Not a logically valid argument. (1 mark) 17. a T, b T, c F, d T, e T, f F, g T, h T (1 mark for each correct value) – – – – – – – – Note: Award (A1) for each correct answer. 18. (a) 2x = 2 = 1 (2 marks) x
(ii) ¬(p  q) alternatively ¬p  ¬q (1 mark) (b) ¬p ¬p  q F T F F T T T T (2 marks – 1 for each column). 16. (a) (i) ¬q  ¬p (1 mark) (ii) q  (p  r) (1 mark for q and 1 mark (p  r) for WITH parentheses) (b) If Alex does not play the flute then it is not true that he is a scientist or from Uruguay. OR If Alex does not play the flute then he is neither a scientist nor from Uruguay. (1 mark for ‘if…then…, 1 mark for antecedent, 1 mark for consequent) (c) q  p ¬(q  p) ¬r  ¬(q  p) T F T T F F T F T T F F T F T T F F F T T F T T (1 mark for each correct column – total of 3 marks) Not a logically valid argument. (1 mark) 17. a – T, b – T, c – F, d – T, e – T, f – F, g – T, h – T (1 mark for each correct value) Note: Award (A1) for each correct answer. 18. (a) 2x = 2 x = 1 (2 marks)