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Consider the following set of propositions

1. I carry an umbrella only if it rains.

2. If I carry an umbrella I use it.

3. I get wet in rain only if I don't use umbrella.

4. It rains today.

Possible Conclusion is:

A. I will not get wet today.

B. I will get wet today.

C. I might get wet today.

D. None of the above.

2 Answers

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p1: I carry an umbrella only if it rains
p2: If I carry an umbrella I use it.
p3: I get wet in rain only if I don't use umbrella.
p4: It rains today

p1: I carry an umbrella - > it rains today
p2: i carry an umbrella -> I use umbrella
p3: I get wet in rain -> I don't use umbrella

I think (C) is correct now, "I might get wet today."  because it rains today doesn't prove that i will not get wet today.

 

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So consider these above as different propositions. If we do conjuction (^) of all these propositions then it gives us the conclusion. Obviously we have to take certain variables and predicates. 

At the end we will be left with two conclusions

  1. it rains and I don’t carry umbrella
  2. it rains and I don’t get wet. 

From 1st we can say if it rains and person is not carrying the umbrella then he can get wet

From 2nd we can say the person gets wet

Thus person can/cannot get wet  i.e. he might get wet. Hence option C is correct

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