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I have been given this question and I have no idea how to tackle it at all.

any help will be super helpful

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    $X = \{ 0, 3, 5, 7, 10 \}$. – 2017-02-27
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    $Y = \{ 1, 2, 4, 7, 8, 11 \}$. – 2017-02-27
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    It is only a matter of counting... – 2017-02-27

2 Answers 2

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There are many possible encodings, but I'll give an example. If the universal set $E=\{0,1,2\}$, then you can represent subsets with binary strings of length $3$. In particular, we can let $110$ mean the following:

  • the first bit $(1)$ represents that $0$ is in the set.
  • the second bit $(1)$ represents that $1$ is in the set.
  • the third bit $(0)$ represents that $2$ is not in the set.

So, $110$ corresponds to $\{0,1\}$. Similarly, $011$ represents $\{1,2\}$. Now, there are other encodings, e.g., the bits could represent the elements of the universal set in a different order.

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$E$ has size $12$ hence you can represent any of its subset by a binary string of length $12$. The first (from the left) bit will represent the presence of $0$ in the subset, the second is for the presence of $1$, etc.

Hence the representation of $A$ is $110101101000$.

Since $A\cup B=\{0,1,3,5,6,8,10,11\}$ then its string representation is $110101101011$.

I think that you have now understood how it works...