Translate the following arguments into standard-form categorical syllogisms. The

Question

Translate the following arguments into standard-form categorical syllogisms. Then use Venn diagrams to determine whether each is valid or invalid.

a) Whenever the average age of people in the U.S. increases, we can infer that they are watching their diets and getting exercise. Accordingly, since the average age of Americans has increased in recent years, we can infer that people are watching their diets and getting exercise.

b) All politicians except Mario Cuomo are nervous about the abortion issue. Hence, Jake Pickle is nervous about the abortion issue because Jake Pickle is not Mario Cuomo.

c) Not all clever animals will survive. Foxes are clever animals. Thus, they are not survivors.

d) Members of the U.S. Congress cannot reject the political consequences of accepting money from unpopular groups to finance their campaigns unless they are willing to suffer the political consequences. Whoever accepts money from political action committees that support racist ideologies rejects the political consequences of accepting money from unpopular groups. Hence, whoever accepts money from political action committees that support racist ideologies is willing to suffer the political consequences.

e) The only musicians who have consciences perform at benefit concerts. Hence classical musicians never perform at benefit concerts, since classical musicians never have consciences.

Explanation / Answer

(a) Whenever the average age of people in the U.S. increases, we can infer that they are watching their diets and getting exercise. Accordingly, since the average age of Americans has increased in recent years, we can infer that people are watching their diets and getting exercise.

Standard Form:

People are watching their diets;

People are getting exercise;

Therefore, average age of people in US increases.

Validity: This statement is valid.

(b) All politicians except Mario Cuomo are nervous about the abortion issue. Hence, Jake Pickle is nervous about the abortion issue because Jake Pickle is not Mario Cuomo.

Standard Form:

Mario Cuomo is a politician;

All Politicians are nervous about the abortion issue but Mario Cuomo is not nervous about the abortion issue;

Jake Pickle is not the same person as Mario Cuomo;

Therefore, Jake Pickle is nervous about the abortion issue.

Validity: This statement is invalid because we do not know if Jake Pickles is a politician.

(c) Not all clever animals will survive. Foxes are clever animals. Thus, they are not survivors.

Standard Form:

Foxes are clever animals;

All clever animals do not survive;

Therefore, Foxes will not survive.

Validity: Since foxes could be among those clever animals who survive, therefore, this statement is invalid.

(d) Members of the U.S. Congress cannot reject the political consequences of accepting money from unpopular groups to finance their campaigns unless they are willing to suffer the political consequences. Whoever accepts money from political action committees that support racist ideologies rejects the political consequences of accepting money from unpopular groups. Hence, whoever accepts money from political action committees that support racist ideologies is willing to suffer the political consequences.

Standard Form:

Members of the U.S. Congress cannot reject the political consequences of accepting money from unpopular groups to finance their campaigns unless they are willing to suffer the political consequences;

Members of the U.S. Congress who accepts money from political action committees that support racist ideologies rejects the political consequences of accepting money from unpopular groups;

Therefore, members of the U.S. Congress who accepts money from political action committees that support racist ideologies is willing to suffer the political consequences.

Validity: This statement is invalid.

(e) The only musicians who have consciences perform at benefit concerts. Hence classical musicians never perform at benefit concerts, since classical musicians never have consciences.

Standard Form:

The only musicians who have consciences perform at benefit concerts;

Cassical musicians do not have consciences;

Therefore, classical musicians never perform at benefit concerts.

Validity: This statement is valid.

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