Q:

Induction question regarding Universe

I was given a question that looks like this.
Prove that for each $2 \le n\in \mathbb N$, if $X_1,\ldots,X_n$ are subsets of some universe $U$, then the following is true:
$$(X_1 \cup\cdots\cup X_n)^c = X_1^c \cap \cdots\cap X_n^c.$$
I am so confused i was staring at this question for at least 2 hours and have no idea how to move forward or what exactly does this mean. 
​​

A:

You can prove this via induction: Let $X_1, \ldots X_n$ be subsets of a universe $U$.

Base case: $n = 2$: $$(X_1 \cup X_2)^C  = X_1^C \cap X_2^C ,$$ which is true by De Morgan's Law. This can be easily proven through a Venn diagram.
Assume that this equality is true for $n = k$, i.e. 
$$(X_1 \cup \cdots \cup X_k)^C = X_1^C \cap \cdots \cap X_k^C.$$
Try to prove (considering the above equality as true) that the equality holds for $n = k+1$.

