Determine whether a set is Invariant, Positively invariant or negatively invariant

I have just started a dynamical systems course and I am a bit confused as to how to determine if something is positively or negatively invariant, or just invariant.

I know the defintions for invariance are as follows:

Let $B subset X$.

$B$ is called
Positively Invariant if $S_tBsubset B$ for all $t geq 0$

B is called negatively invariant if $S_tBsupset B$

B is called invariant if $S_tB=B$ for all $tgeq 0$

Here are some questions I am stuck on:

Considering the continuous time dynamical system given by the ODE $x’=-x$
with solution $x(t)=xe^{-t}$, determine if the following sets are invariant, positively or negatively invariant.

1.) $M subset mathbb R : M=(0,1)$

So, I have that $S_t((0,1))=(0,-e^{-t})notsubset B=(0,1)$ for all $t>0$

Then, for $t=0$, we have $S_t((0,1))=(0,-1)notsubset(0,1)$ for all $t=0$.

Hence, I cannot see how this is invariant at all? None of the defintions apply here or have I done it all wrong?

2.) $[-1,1]$

I have that this one is positively invariant as $S_tx=xe^{-t} in [1,1]$ for all $t geq 0$ and $xin[-1,1]$

3.) (1,2)

I have this as invariant.

Any help on these much appreciated. Surprisingly few other examples or resources on this on line.