Question

D and E are sets of real numbers defined as follows.D=v E = {v | v<)Write Dn E and DU E using interval notation.If the set is empty, write Ø.D n E=D u E=

Answer 1

The first step we have to follow is to write the sets in interval notation.

D contains all the numbers that are greater than 4.

E contains all the number that are less than or equal to 9.

In interval notation, they are written this way:

`\begin{gathered} D=(4,\infty) \\ E=(-\infty,9\rbrack \end{gathered}`

Now, to find D∩E, we have to find the set of values that both sets have in common. That set is compound of the number that are greater than 4 and less than or equal to 9. It means that this set is:

`D\cap E=(4,9\rbrack`

To find D∪E, we have to find the set of values that is formed when these sets are put together. That set is compound of all the real numbers. It means that this set is:

`D\cup E=(-\infty,\infty)`