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The region enclosed by the inequalities x + y ≤ 1 and x − y ≤ 1 lies in which quadrants?

1. I and II
2. I and III
3. II and III
4. All four quadrants

Correct answer: All four quadrants

Solution

The region x+y<=1 and x-y<=1 is unbounded. Sample points (0.4,0.4), (-1,1), (-1,-1), (0.5,-0.4) all satisfy both inequalities, so the region lies in all four quadrants.

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