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PART a Some Playoff Games Are Heartbreakers, Since All Playoff

Question 365

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PART A Some playoff games are heartbreakers, since all playoff games are either heartbreakers or occasions for glee.
Which of the following correctly expresses the form of this argument? a. All P are either H or O Some P are H.\begin{array} { l } \text {All \( \mathrm{P} \) are either \( \mathrm{H} \) or \( \mathrm{O} \). }\\ \hline\text { Some P are \( \mathrm{H} \).}\\\end{array}\quad b.  Some P are H. All P are either H or O.\begin{array} { l } \text { Some P are \( \mathrm{H} \).}\\ \hline\text { All \( \mathrm{P} \) are either \( \mathrm{H} \) or \( \mathrm{O} \).}\\\end{array}

c. All P are either H or O Some PG are H\begin{array} { l } \text {All \( \mathrm{P} \) are either \( \mathrm{H} \) or \( \mathrm{O} \). }\\ \hline\text { Some \( \mathrm{PG} \) are \( \mathrm{H} \). }\\\end{array}\quad d. All P are H  Some P are either H or O.\begin{array} { l } \text {All \( \mathrm{P} \) are \( \mathrm{H} \) }\\ \hline\text { Some \( \mathrm{P} \) are either \( \mathrm{H} \) or \( \mathrm{O} \).}\\\end{array}

e. All PG are either H or O Some G are H.\begin{array} { l } \text {All \( \mathrm{PG} \) are either \( \mathrm{H} \) or \( \mathrm{O} \). }\\ \text { Some \( \mathrm{G} \) are \( \mathrm{H} \).}\\\end{array} PART B
Which of the following substitutions proves the argument invalid?
A) P = fish, H = animals, O = mammals.
B) P = dogs, H = cats, O = fish.
C) P = dogs, H = fish, O = animals.
D) P = male, G = dogs, H = animals, O = fish.
E) P = women, H = humans, O = doctors.

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