Question

D and E are sets of real numbers defined as follows.D={ww<3)E={ww26)Write D U E and Dn E using interval notation.If the set is empty, write Ø.

Answer 1

`\begin{gathered} D=\lbrace w|w<3\rbrace \\ E=\lbrace w|w\ge6\rbrace \end{gathered}`

To solve the given operations you can graph each inequality:

D:

E:

The Union of D and E: To solve this operation you draw both inequalities in the same number line:

In interval notation you get: When the inequality sing is < or > you use a normal parentheses ( ), when the inequality sing is ≥ or ≤ you use a square paretheses [ ], with the infinite number you use always a normal parentheses ( ):

`D\cup E=(-\infty,3)\cup\lbrack6,\infty)`

The intersection of D and E: Intersection means the part that both inequalities share. In this case as you can see in the graph of each inequality therea are no numbers that are included in both inequalities then the interseption is empty:

`D\cap E=\varnothing`