Consider the two statements below:

Statement $1$: $$x in Z$,[(3$x $-5>0)(2-$ x$2>=1)]$

Statement $2$: $$x in Z$+,[($x$2-3<0)(3$x $-4>=0)].$

Which one of the following alternatives is TRUE regarding statements $1$ and $2?$

Select one:

a$.$

Statement $1$ is false and statement $2$ is true.

b$.$

Both statements $1$ and $2$ are false.

c$.$

Statement $1$ is true and statement $2$ is false.

d$.$

Both statements $1$ and $2$ are true.