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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→
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.
3
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 Summer '00
 Aula4IntroducaoC
 Logic, Assumption of Mary, The Cook, Pope Pius XII, Roman Catholic Mariology

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