Measure theory problems. Prove or disprove the following:
a)If $\mathscr A$ is a $σ$-Algebra on $Ω$ then {$Ω$ \ $A$ : $A$ element of $\mathscr A$} too.
b)A $σ$-Algebra with 3 elements exists.
c)A measure $μ$ on $P(\mathbb R)$ with $μ$({x}}=$1$ exists.

a) Isn't this equal to Ω \ $\mathscr A$? If so then this is the second property of a $σ$-Algebra.
b) Ω={1,2,3}, $\mathscr A$={{1},{2},{3}} is right? 
c) I don't know I just know that for a Lebesgue-Measure $μ$({x}} is equal to $0$. Don't know if any measure exists that can satify c).

a) A $\sigma$-algebra is stable under complementation, hence $\{\Omega\setminus A,A\in\mathcal A\}=\mathcal A$ (it cannot be equal to $\Omega\setminus \mathcal A$, because $\mathcal A$ is a class of subsets of $\Omega$, while $\Omega$ is a set. 
b) Your $\mathcal A$ is not a $\sigma$-algebra (it should at least contain $\Omega$). If $\mathcal A$ is a $\sigma$-algebra with more than two elements, there is $A\in\mathcal A$ which is neither the whole set nor empty. But this is also the case for $\Omega \setminus A$.
c) Consider the counting measure (which assigns to each sets its number of elements if the set if finite, and $+\infty$ otherwise). 
