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Represent the following set of points in the XY plane:

{ (x,y) | |x|=1 }

{ (x,y) | |x| is less than or = 1 }

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Where do you get stuck? Can you draw the set where $x = 1$ or $x = -1$? – mrf Jun 9 '12 at 22:24
yes its the answer for the first question right? – mgh Jun 9 '12 at 22:28
It is. Now for the second one, this also includes lines such as $x = 1/2$, $x = -1/3$ or more generally lines $x = a$ for every $a$ with $-1 \le a \le 1$. Can you draw it now? – mrf Jun 9 '12 at 22:30
for the second one, will the line start from -1 till 1 on the x axis – mgh Jun 9 '12 at 22:34
You may want to read about why should we accept answers and how do we do that. Your accept ratio is less than 40% which is less than acceptable on this site. – Asaf Karagila Jun 9 '12 at 22:35
up vote 1 down vote accepted

HINT: Note that your set imposes no restriction at all on the $y$-coordinate. If you find a point in the set, every other point with the same $y$-coordinate will also be in the set. Now, what does $\{x\in\Bbb R:|x|\le 1\}$ look like as a subset of the real line?

Added: Your region is the blue stripe in the picture below; it extends infinitely far up and down. enter image description here

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for the second one, will the line start from -1 till 1 on the x axis – mgh Jun 9 '12 at 22:40
@meg_1997: That’s right, and it will include both endpoints, $-1$ and $1$. Thus, your region in the plane will be an infinite vertical stripe running between the lines $x=-1$ and $x=1$. – Brian M. Scott Jun 9 '12 at 22:42
is it possible to show it on graph here by you – mgh Jun 10 '12 at 0:05
@meg_1997: I can produce a rough picture; hang on for a few minutes while I do it. – Brian M. Scott Jun 10 '12 at 0:09
hey thanks for that:) – mgh Jun 10 '12 at 0:21

Hint: Can you represent them on the $x$ axis? Note that since the criteria do not depend on $y$ the sets will be vertical lines at all $x$ that are acceptable.

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