# Logic

Claudia has four home works to do, go to the market, study for the exam, clean the room, and practice sports, she knows that:
-she goes to the market if she studies for the exam.
-she studies for his exam if she does not clean his room
-if she does not practice his sport then she does not go to the market

between the next affirmations the only that can be deduced logically is:
a)if she does not go to the Market then she does not practice sport
b)She practice sport if she prepares the exam
c)She practice the sport if she does not go to the market
d)If she cleans her room then she go to themarket

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1. If we let
a = she studies for the exam
b = she goes to the market
c = she cleans her room
d = she practices her sport

I) a -> b
II) ~c -> a
III) ~d -> ~b

A) ~b -> ~d
B) a -> d (yes - transitivity)
C) ~b -> d
D) c -> b

B is true because the contrapositive of III is b -> d

So, a -> b -> d

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posted by Steve

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