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
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
To deduce the logical statement, let's break down the given information:
1) She goes to the market if she studies for the exam.
- This means that studying for the exam is a prerequisite for going to the market.
2) She studies for her exam if she does not clean her room.
- This implies that if her room is not clean, she prioritizes studying for her exam over cleaning.
3) If she does not practice her sport, then she does not go to the market.
- This suggests that practicing her sport is necessary for her to go to the market.
Now, let's analyze the answer options:
a) If she does not go to the market, then she does not practice sports.
- There is no direct connection between not going to the market and not practicing sports based on the given information. This statement cannot be deduced logically.
b) She practices sports if she prepares for the exam.
- There is no given information connecting practicing sports and preparing for the exam. This statement cannot be deduced logically.
c) She practices sports if she does not go to the market.
- From statement 3, we know that if she does not practice sports, she does not go to the market. Therefore, we can deduce that if she does not go to the market, she practices sports. This statement can be deduced logically.
d) If she cleans her room, then she goes to the market.
- There is no given information connecting cleaning her room and going to the market. This statement cannot be deduced logically.
Therefore, the only statement that can be deduced logically is:
c) She practices sports if she does not go to the market.