All flowers are roses. $\equiv$ For all $x$ , if $x$ is a flower then it has to be a rose $\equiv$ $\forall x$($ f(x) \rightarrow r(x))$$\equiv$ $\forall x$$(\sim f(x)\ V r(x))$

No rose is a flower.$\equiv$ There does not exist an $x$ such that $x$ is a rose and it is a flower $\equiv$ $\sim \exists x ( r(x) \Lambda f(x))$ $\equiv$ $\forall x$$(\sim r(x)\ V \sim f(x) )$

No flower is a rose.$\equiv$ There does not exist $x$ such that $x$ is a flower and it is a rose $\equiv$ $\sim \exists x ( f(x) \Lambda r(x))$ $\equiv$ $\forall x$$(\sim f(x)\ V \sim r(x) )$

Some flowers are roses$\equiv$ There exists some $x$ such that $x$ is a flower and it is a rose $\equiv$ $\exists x(f(x) \Lambda r(x))$

No rose is not a flower.$\equiv$ There does not exist $x$ such that $x$ is a rose and it is not a flower $\equiv$$\sim \exists x( r(x) \Lambda \sim f(x))$ $\equiv$ $\forall x$$(\sim r(x)\ V f(x))$

All roses are flowers. $\equiv$$\forall x$( if $x$ is a rose then it is a flower)$\equiv$ $\forall x$$( r(x) \rightarrow f(x))$ $\equiv$ $\forall x$$(\sim r(x)\ V f(x))$$\equiv$