Final answer:
The correct word to complete the sentence is 'or,' indicating a choice between two mutually exclusive actions: studying hard for an exam or facing the possibility of failure. The use of 'or' facilitates the process of deduction in decision-making.
Step-by-step explanation:
The correct answer to the question 'You can study hard for this exam _______ you can fail.' is 'or.' This conjunction is used to connect two alternative statements, implying that if one of the actions is not chosen or does not occur, the other action is the inevitable result. The statement 'You can study hard for this exam or you can fail' suggests that by not studying hard, failure is a possible outcome. It presents a choice between two mutually exclusive outcomes. Using 'or' in arguments allows for the use of deduction. For instance, if one of the two statements connected by 'or' is proven to be false, you can deduce that the other must be true. Such reasoning is vital for making informed decisions and understanding the consequences of actions.