Describe explicitly the $M$-measurable functions in case $M$ is one of the following $\sigma$-algebras:

Describe explicitly the $M$-measurable functions in case $M$ is one of the
following $\sigma$-algebras:

Describe explicitly the $M$-measurable functions in case $M$ is one of the
following $\sigma$-algebras:
(a) $M=\{\emptyset,X\}$
(b) $M=2^{X}$
(c) For certain disjoint sets $E_1,...,E_N$, $X=\cup_{k=1}^N E_k$, and $M$
is the algebra (in fact, $\sigma$-algebra) generated by the collection of
sets $\{E_1,...,E_N\}$.
Here's my book's definition of $M$-measurable:
Suppose $f:X\to[-\infty,\infty]$. Then $f$ is $M$-measurable if for all
$t\in[-\infty,\infty]$ the set $f^{-1}([-\infty,t])$ belongs to $M$. Inn
other words, $\{x\in X|f(x)\le t\}\in M$.
Of course, the form of the inequality $f(x)\le t$ is arbitrary.
Thanks.