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

C$.$ I go to Paris if and only if I visit the Eiffel Tower.

D$.$ I go to Paris and I visit the Eiffel Tower.

E$.$ I visit the Eiffel Tower

Which proposition is a necessary condition for the following statement to be true: $"$n is divisible by $6$ and n is not divisible by both $2$ and $3."$

A$.$ n is divisible by $6$

B$.$ n is not divisible by $6$

C$.$ n is divisible by both $2$ and $3$

D$.$ n is divisible by $6$ and n is divisible by both $2$ and $3.$

E$.$ n is divisible by $6$ if and only if n is divisible by both $2$ and $3.$

Which proposition is a sufficient condition for the following statement to be true: $"$If I am on time for work then I catch the $8$:$05$ bus."

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

B$.$ If I catch the $8$:$05$ bus then I am on time for work.

C$.$ I am late for work

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

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

F$.$ I miss the $8$:$05$ bus

G$.$ I am on time for work

Rewrite the following as an equivalent if then statement: $"\text{'}$I vote in the election' is a necessary condition for 'I feel enfranchised'."

A$.$ If I feel enfranchised then I vote in the election.

B$.$ If I vote in the election then I feel enfranchised.

C$.$ If I feel disenfranchised then I vote in the election.

D$.$ If I don't vote then I feel disenfranchised.

E$.$ If I feel enfranchised then I don't vote.

F$.$ If I vote in the election then I feel disenfranchised.

G$.$ If I don't vote then I feel enfranchised.

H$.$ If I feel disenfranchised then I don't vote.

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

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

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

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

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

E$.$ If n is prime then n is even but not $2.$

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

G$.$ If n is even but not $2$ then n is prime.

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

Rewrite the following as an equivalent if then statement: $"\text{'}$I feel enfranchised' is a sufficient condition for 'I vote in the election'."

A$.$ If I don't vote then I feel disenfranchised.

B$.$ If I don't vote then I feel enfranchised.

C$.$ If I vote in the election then I feel enfranchised.

D$.$ If I feel enfranchised then I vote in the election.

E$.$ If I feel disenfranchised then I vote in the election.

F$.$ If I feel disenfranchised then I don't vote.

G$.$ If I feel enfranchised then I don't vote.

H$.$ If I vote in the election then I feel disenfranchised.