1.

Plot the region satisfying |x|+ |y| le 2 and |x|+|y| gt 2.

Answer»

Solution :`|x|+ |y| le 2`
`therefore ""{{:(x+y le2",",, x ge 0"," y ge0), (x-y le 2",",, x ge 0"," y le0), (-x+y le 2",",,x le 0 ","y ge 0 ),(-x-y le 2",",,x le0 ","y le 0):}`
For `x ge 0, y ge0 and x+y le 2`, we have the following region.

Similarly, we have other three triangles, one in each quadrant.
Clubbing all four cases, we have the following region as a square.

Clearly, the POINTS satisfying `|x|+ |y| GT 2` LIE OUTSIDE the square.


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