IGNOU MTE 12 2018 - Test for convexity the following sets:S = {(x, y) | x2 + y2 >1, y

Question

Test for convexity the following sets:
S = {(x, y) | x² + y² >1, y > x, y > - x}
S = {(x, y) | x² + y² <16, x < 2, y > 2}

14 Feb 2018

Answer :

Word Count : 420

For a set to be convex, any line segment joining two points in the set must lie entirely within the set. We test each set accordingly. Set 1: $S = \{(x, y) \mid x^2 + y^2 > 1, y > x, y > -x\}$ * The condition $x^2 + y^2 > 1$ describes the region outside a circle of radius 1. * The conditions $y > x$ and $y > -x$ describe the region above the lines $y = x$ and $y = -x$, forming a wedge above the x-axis. Take two points in $S$, e.g., $A = (2, 2)$ and

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