# Basic Set Theory problem

So i'm relatively new to computer science and have been learning set theory and am stumped on a question in it.

The question specifies that we're only looking at subsets of universe U = {0,...,n-1}. For a set S ⊆ U, the characteristic vector denoted by Xs is an n-bit string where j is 1 if and only if j ∈ S. Example, n = 4, S = {1, 3} Xs = 1010.

it is asking what is XØ and XU. I think I am completely overthinking this but I can't figure out what XØ and XU are referring to.

Characteristic vector is a string representation of a set in this case. For a set $$S$$, the characteristic vector is denoted by $$X_S$$. $$X_\emptyset$$ and $$X_U$$ are referring to the characteristic vector of $$U$$ (Universal set) and $$\emptyset$$ (Empty set) respectively. In your example, $$\text{If }n = 4 \text{ and } S = \{1, 3\} \text{, then } X_s = 1010.$$ We simply need to replace $$S$$ with a set $$\{0, 1, 2, \dots n-1\}$$ to find $$X_U$$ and with $$\{\} = \emptyset$$ to find $$X_\emptyset$$. I think you can leave $$n$$ as a variable unless it is fixed to some value.