.Is it possible to use the Law of Detachment to draw a conclusion?
I will go to the cinema if and only if I can afford to buy a ticket. The movie starts at 7:30.
Yes, it is possible.
No, it is not possible.
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Are you asking that, if you are given the correct statement that "I will go to the cinema if and only if I can afford to buy a ticket", and then you are given the information "the movie starts at 7:30", and now asked to decide that, based on this information, and the statement, can you make a conclusion about whether or not you will go to the cinema? If that's what you are asking, then, no you can't make a conclusion. The information about what time the movie starts has nothing to do with the statement ("I will go to the cinema if and only if I can afford to buy a ticket"), so you can't use it. But I'm not sure if that's what you are asking.