Question

B and C are sets of real numbers defined as follows.

Answer 1

In the picture we have a plot of the sets B (in blue) and C (in red).

We can write the sets in the interval notation:

`\begin{gathered} B=(-\infty,3\rbrack \\ C=(5,\infty) \end{gathered}`

Q) We want to calculate the union and the intersection of those sets.

A)

1) B U C = union of B and C

The union of B and C sets are all the elements that belongs to B or C. Using the sets written in interval notation we see that:

`B\cup C=(-\infty,3\rbrack\cup(5,\infty)`

2) B ∩ C = insersection of B and C

The inserction of B and C sets are all the elements that belongs to B and C at the same time. From the graph of above we see that there are not elements that belongs to B and C at the same time, so the inserction does not has any elements, so the intersection of the sets is the emphy set (∅):

`B\cap C=\varnothing`

So, in summary the answer is:

`\begin{gathered} B\cup C=(-\infty,3\rbrack\cup(5,\infty) \\ B\cap C=\varnothing \end{gathered}`