$2$ Is it a Subtype?

Task $2\mathrm{.}1(15$ points$).$

For each pair of types below, say whether it is safe for ${}_1$ type to be considered a subtype of ${}_2.$

Your answer should start with a clear "yes" or $"$no$"($or "safe"$/"$unsafe$"$ or similar$),$ but also explain your answer briefly but clearly. Note that this is not asking you whether the subtyping relation is allowed by the rules we gave in class: if a particular pair below is correct from the rules we gave in class, this is definitely safe as we proved the rules sound; however, there are other safe subtyping relations we didn't talk about in class. Think about the various intuitive explanations we gave for what it means to be a subtype.

int nat

int real $($where real is the type of real numbers$)$

int $$ nat $$ string int $$ int

int $$ string $$ string int $$ int

bool unit $+$ unit $+$ unit

unit bool

bool nat

int : unit

void : unit

int $$ int nat $$ int