I have been asked the following questions on a tutorial worksheet and am not sure how to answer.
"There is a natural relationship between sets and bit strings which is called the characteristic vector for a set. We'll look only at subsets of the universe $U = \{0,\ldots,n-1\}$ for some $n$, but the concept can be generalised to arbitrary sets. For a set $S\subseteq U$, the characteristic vector is denoted by $X_s$ and is an $n$-bit string where bit $j$ is $1$ if and only if $j\in S$. For example, with $n = 4$ and $S = \{1,3\}$ we have $X_s = 1010$."
Question: Given $X_s$ and $X_t$, what is the characteristic vector of $S\cap T$?
any clues would be greatly appreciated.