Select ALL the correct answers.

$1)$ Which of the following are NOT prepositions?

a$)$ Greenville is in NC$.$

b$)$ Greenville is the capitol of NC$.$

c$)1+0=1$

d$)$ x $+0=2$

e$)$ Sit down!

f$)$ What is your name?

$2)$ Which of the following is true if the conditional statement P $$ Q is true?

a$)$ The converse is Q $$ P$,$ and it is true

b$)$ The inverse is $$P $->$Q$,$ and it is true

c$)$ The contrapositive is $$Q $->$P$,$ and it is true

d$)$ All the above statements are true

$3)$ Consider the following prepositions

P: Sam is a CS graduate

Q: Mary is a CS graduate

R: Demi is a CS graduate

A: Sam studied Data Structure

B: Mary studied Data Structure

C: Demi studied Data Structure.

Suppose the implications P $$ A$,$ Q $$ B$,$ R $$ C and the prepositions $$Q$,$ C$,$ and $$A are all true.

Which of the following is true?

a$)$ Mary did not study Data Structures $($B is true$)$

b$)$ Demi studied Data Structure, therefore, Demi is a CS graduate $($R is true$)$

c$)$ Sam is not a CS graduate $($P is true$).$

d$)$ All the above are true.