What is the negation of the following: $"$If it rains then I take an umbrella."

A$.$ If it rains then I take an umbrella.

B$.$ It rains or I don't take an umbrella.

C$.$ If I don't take an umbrella then it doesn't rain.

D$.$ It rains and I don't take an umbrella.

E$.$ It rains and I take an umbrella.

F$.$ It doesn't rain and I don't take an umbrella.

G$.$ It rains or I take an umbrella.

H$.$ It doesn't rain or I take an umbrella.

I. If I take an umbrella then it rains.

J$.$ If it doesn't rain then I take an umbrella.

K$.$ If it doesn't rain then I don't take an umbrella.

What is the negation of the following: $"$If n is prime then n is odd or n is $2."$

A$.$ If n is composite then n is even but not $2.$

B$.$ n is composite and n is odd or n is $2.$

C$.$ n is prime or n is odd or n is $2.$

D$.$ n is prime or n is even but not $2.$

E$.$ n is prime and n is even but not $2.$

F$.$ n is prime and n is odd or n is $2.$

G$.$ If n is odd or n is $2$ then n is prime.

H$.$ If n is prime then n is odd or n is $2.$

I. n is composite or n is odd or n is $2.$

J$.$ If n is even but not $2$ then n is composite.

K$.$ If n is composite then n is odd or n is $2.$

What is the negation of the following statement: "I am on time for work and I catch the $8$:$05$ bus."

A$.$ I am on time for work and I catch the $8$:$05$ bus.

B$.$ I am on time for work and I miss the $8$:$05$ bus.

C$.$ I am late for work or I catch the $8$:$05$ bus.

D$.$ I am on time for work or I miss the $8$:$05$ bus.

E$.$ I am late for work and I catch the $8$:$05$ bus.

F$.$ I am late for work and I miss the $8$:$05$ bus.

G$.$ I am on time for work or I catch the $8$:$05$ bus.

H$.$ I am late for work or I miss the $8$:$05$ bus.

What is the negation of the following statement: $"$n is prime or n is odd or n is $2."$

A$.$ n is prime and n is odd or n is $2.$

B$.$ n is composite or n is even but not $2.$

C$.$ n is composite or n is odd or n is $2.$

D$.$ n is prime or n is even but not $2.$

E$.$ n is composite and n is odd or n is $2.$

F$.$ n is composite and n is even but not $2.$

G$.$ n is prime and n is even but not $2.$

H$.$ n is prime or n is odd or n is $2.$

What is the converse of the following: $"$If I form a study group then I raise my grades."

A$.$ If I raise my grades then I form a study group.

B$.$ If I form a study group then I raise my grades.

C$.$ If I lower my grades then I work alone.

D$.$ If I form a study group then I lower my grades.

E$.$ If I raise my grades then I work alone.

F$.$ If I work alone then I lower my grades.

What is the inverse of the following: $"$If I am hungry then I eat an apple."

A$.$ If I eat an apple then I am hungry.

B$.$ If I am hungry then I eat an apple.

C$.$ If I$\text{'}$m not hungry then I don't eat an apple.

D$.$ If I don't eat an apple then I$\text{'}$m not hungry.

E$.$ If I eat an apple then I am not hungry.

F$.$ If I$\text{'}$m hungry then I eat an apple.

What is the contrapositive of the following: $"$If I go to Paris then I visit the Eiffel Tower."

A$.$ If I don't go to Paris then I visit the Eiffel Tower.

B$.$ If I go to Paris then I visit the Eiffel Tower.

C$.$ If I don't visit the Eiffel Tower then I don't go to Paris.

D$.$ If I don't visit the Eiffel Tower then I go to Paris.

E$.$ If I visit the Eiffel Tower then I go to Paris.

F$.$ If I don't go to Paris then I don't visit the Eiffel Tower.