# Characteristic Vector Question

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.

• Why not compute some examples, and see whether you can figure it out? – Gerry Myerson Mar 24 at 8:53
• yeah i did sort this. just reading the questions in the incorrect way. Xs & Xt – Malkeir Mar 24 at 9:36
• Or you can multiply them componentwise – mathpadawan Mar 24 at 16:24