L04-problemsHO-Sol (1)

# B either randy or paul but not both are chatting c if

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b. Either Randy or Paul but not both are chatting. c. If Abby is chatting, so is Randy d. Paul and Kevin are either both chatting, or neither is. e. If Heather is chatting than so are Abby and Kevin. Let A = Abby is chatting, H = heather is chatting, K = Kevin is chatting, P = Paul is chatting, R = Randy is chatting The premises are: (1) K V H (2) R P 2

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(3) A R (4) P K (5) H (A Λ K) We start with making an assumption. If the assumption leads to a contradiction, than the negation of the assumption is true. However if the assumption does not lead to a contradiction, we cannot conclude anything. Assume H is true (6) H From (6) and (5) by MP we conclude (7) A (8) K From (8) and (4) we conclude (9) P From (7) and (3) we conclude (10) R From (10) and (2) we conclude (11) ~P This contradicts (9), therefore our assumption is false. Therefore we can conclude ~H: Heather is not chatting (12) ~H From (12) and (1) by DS we conclude (13) K From (13) and (4) we conclude (14) P From (14) and (2) we conclude (15) ~R From (15) and (3) we conclude (16) ~A Thus we have determined that Kevin and Paul are chatting, and the other three individuals are not chatting.
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• Summer '00
• Aula4-IntroducaoC
• Logic, Assumption of Mary, The Cook, Pope Pius XII, Roman Catholic Mariology

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