Which proposition is a necessary condition for the following statement to be true: "I don't go to Paris and I visit the Eiffel Tower."

A. I do not visit the Eiffel Tower.
B. I go to Paris and I visit the Eiffel Tower.
C. I go to Paris
D. I visit the Eiffel Tower
E. I go to Paris if and only if I visit the Eiffel Tower.

Which proposition is a necessary condition for the following statement to be true: "I form a study group and I lower my grades."

A. I form a study group if and only if I raise my grades.
B. I form a study group and I raise my grades.
C. I raise my grades
D. I work alone
E. I form a study group

Which proposition is a sufficient condition for the following statement to be true: "If I form a study group then I raise my grades."

A. I work alone
B. I form a study group and I lower my grades.
C. If I raise my grades then I form a study group.
D. I form a study group or I raise my grades.
E. I form a study group
F. I work alone or I lower my grades.
G. I lower my grades

Rewrite the following as an equivalent if then statement: "'I go to Paris' is a necessary condition for 'I visit the Eiffel Tower'."

A. If I don't go to Paris then I do not visit the Eiffel Tower.
B. If I don't go to Paris then I visit the Eiffel Tower.
C. If I visit the Eiffel Tower then I go to Paris.
D. If I go to Paris then I do not visit the Eiffel Tower.
E. If I go to Paris then I visit the Eiffel Tower.
F. If I do not visit the Eiffel Tower then I don't go to Paris.
G. If I visit the Eiffel Tower then I don't go to Paris.
H. If I do not visit the Eiffel Tower then I go to Paris.

Rewrite the following as an equivalent if then statement: "'n is odd or n is 2' is a necessary condition for 'n is prime'."

A. If n is composite then n is odd or n is 2.
B. If n is prime then n is odd or n is 2.
C. If n is odd or n is 2 then n is composite.
D. If n is even but not 2 then n is prime.
E. If n is composite then n is even but not 2.
F. If n is even but not 2 then n is composite.
G. If n is prime then n is even but not 2.
H. If n is odd or n is 2 then n is prime.

Rewrite the following as an equivalent if then statement: "'I feel tired' is a sufficient condition for 'I exercise'."

A. If I exercise then I feel tired.
B. If I feel tired then I exercise.
C. If I don't exercise then I feel tired.
D. If I feel tired then I don't exercise.
E. If I feel envigorated then I don't exercise.
F. If I don't exercise then I feel envigorated.
G. If I feel envigorated then I exercise.
H. If I exercise then I feel envigorated.