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Given the argument and its Euler diagram, determine the syllogism is valid or invalid. Those who play football. don Football and studying donft mix Those who studt Don is a football player ˆdon does not study

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Determine whether the statement (3) follows from statement (1) and (2) by the law of detachment or the law of syllogism. If it does, state which law was used. If it does not, write invalid. (1) if you study you will be smart (2)

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For t∈R, define the following two functions: f1(t)=12π−−√exp(−max(1,t2)2) and f2(t)=12π−−√exp(−min(1,t2)2). In this problem, we explore whether these functions are valid probability density functions. Determine

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