Question

A and B are sets of real numbers defined as follows.A = xXB = xWrite A UB and An B using interval notation.If the set is empty, write 0.

Answer 1

The given sets are

`\begin{gathered} A=\lbrace x:x,x\leq2\rbrace \\ \\ B=\lbrace x:x,x<7\rbrace \end{gathered}`

That means A is all real numbers from 2 to negative infinity, and B is all real numbers between 7 and positive infinity

`\begin{gathered} A=(-\infty,2] \\ \\ B=(7,\infty) \end{gathered}`

Then we can find the union and intersection

`\begin{gathered} A\cup B=(-\infty,2]\cup(7,\infty) \\ OR \\ A\cup B=(-\infty,\infty)-(2,7] \end{gathered}`

I will draw a sketch to show you the intersection

We can see that there is NO intersection between A and B, then

`\begin{gathered} A\cap B=\lbrace\rbrace \\ A\cap B=0 \end{gathered}`