$\textbf{The Problem:}$ Let $A_1,\dots,A_5$ be events on the same probability space. Express the following events using the usual set operations $\left(^\complement,\bigcap,\bigcup\right)$ and the events $A_k$ for $1\leq k\leq 5.$
$\textbf{a)}$ None of the five events $A_k$ for $1\leq k\leq 5$ occur.
Using De Morgan's Law, this event can be expressed as $$\left(\bigcup_{k=1}^5 A_k\right)^\complement=\bigcap_{k=1}^5 A_k^\complement.$$
$\textbf{b)}$ At least two of the five events $A_k$ for $1\leq k\leq 5$ occur.
For this event, I think that we can express it as $$\bigcup_{k\in\mathcal P}A_k\quad\quad\quad\text{for some $\mathcal P\subset\mathbb\{1,\dots,5\}$ with $\#\mathcal P=2.$}$$
$\textbf{c)}$ One or three of the five events $A_k$ for $1\leq k\leq 5$ occur.
For this part, my attempt looks like $$A_j\cup\left(\bigcup_{k\in\mathcal P}A_k\right)\cup\left(\bigcup_{i\ne j,i\notin\mathcal P}A_i\right)\quad\text{where }j\in\{1,\dots,5\},\mathcal P\subset\{1,\dots,5\}\text{ with }\#\mathcal P=3.$$
Could anyone please provide some feedback on my attempted solutions? I am very confident about the first one, but slightly confused about the other two.
Any feedback is much appreciated, and I want to thank you for your time, and wish you a great weekend.