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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.

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

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