To graph: The region provided by the set .
The set, .
The graph of the region provided by the set is sketched in the coordinate plane.
Consider the equation .
Rewrite the equation as,
Recall that the standard form of the equation of the circle is , where denote the center of the circle and r denote the radius.
Compare, and .
Therefore, center of circle is and radius is .
Now, on the Cartesian plane construct a circle with center at origin and radius 1 unit.
Since, the inequality is
Now, shade the common region that lie interior to the circle..
The region obtained is provided below,
The region provided by the set is shaded region. The region shaded forms a circle with center at origin and radius 1 unit. The shaded region is such that for each pair of point the condition should hold true. The region formed above is that radius of circle is less than or equal to 1.
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