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| Who is not rich? (Posted on 2005-06-22) |
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Anne, Bernice and Claudia are three remarkable women, each having some remarkable characteristics.
(1) Just two are intelligent, just two are beautiful, just two are artistic and just two are rich.
(2) No one has more than three characteristics.
(3) Of Anne it is true that : if she is intelligent, she is rich.
(4) Of Bernice and Claudia it is true that: if she is beautiful, she is artistic.
(5) Of Anne and Claudia it is true that: if she is rich, she is artistic.
Who is not rich? (Show your reasoning)
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Submitted by pcbouhid
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Rating: 4.1667 (6 votes)
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Solution:
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(Hide)
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From (3) and (5), if Anne is intelligent she is artistic.
From (5), if Anne is rich, she is artistic.
From (1) and (2), if Anne is neither rich nor intelligent, she is artistic.
So, in any case, Anne is artistic.
From (4), if Claudia is beautiful she is artistic.
From (5), if Claudia is rich she is artistic.
From (1) and (2), if Claudia is neither rich nor beautiful, she is artistic.
So, in any case, Claudia is artistic.
Then, from (1), Bernice is not artistic. Then, from (4), Bernice is not beautiful.
So, from (1) and (2), Bernice is intelligent and rich.
Then, from (1), Anne and Claudia are both beautiful. Then from (2) and (3), Anne is not intelligent; so from (1), Claudia is intelligent.
Then, from (1) and (2), Anne is rich and Claudia is not rich.
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