SOLUTION: Albert has 3 daughters, Kate, Liz and Marina. 2 of them are Blonde and one, Brunette. If kate is Blonde, then so is Elizabeth; If Elizabeth is Blonde then so is Marina. Based on th

Algebra ->  Probability-and-statistics -> SOLUTION: Albert has 3 daughters, Kate, Liz and Marina. 2 of them are Blonde and one, Brunette. If kate is Blonde, then so is Elizabeth; If Elizabeth is Blonde then so is Marina. Based on th      Log On


   

Question 332299: Albert has 3 daughters, Kate, Liz and Marina. 2 of them are Blonde and one, Brunette. If kate is Blonde, then so is Elizabeth; If Elizabeth is Blonde then so is Marina. Based on this information, which of the following is certainly true and why?
a) Liz is Brunette and Kate Blonde
b) Kate is Brunette and Marina Blonde
c) Marina and Elizabeth are Brunettes
d) Kate is Blonde, and Marina is Brunette
e) Kate and Liz are Blonde
Answer by solver91311(24713) About Me  (Show Source):
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Let A represent Kate is Blonde. Let B represent Liz is Blonde. Let C represent Marina is blonde.

If A then B.Given

If B then C.Given

If A then C.Transitivity

But that means if A then B AND C which means that all three are blonde contradicting the given that 2 are blonde and 1 is not. Hence, Kate is not blonde which in turn implies that Liz and Marina are blonde.

Answer b. is the only one that fits.

John

My calculator said it, I believe it, that settles it