$$ Problem $3(30$ points$)$: Consider the set $AP=\{x,Y\}$ of atomic propositions. Formulate the

following properties as LT properties and characterize each of them as being either an invariance,

safety property, or liveness property, or none of these.

a$.$ X should never occur,

b$.$ X should occur exactly once,

c$.x$ and $Y$ alternate infinitely often,

d$.$ X should eventually be followed by Y$.$