In this question we show that certain sets are not convex.

Question

In this question, we show that certain sets are not convex.

For each of the following sets, give the coordinates of two points P and Q which are in the set, but the line from P to Q goes outside the set.

a) {(x1,x2):1≤∣x1∣≤2,∣x2−3∣≤2}

(b) {(x,y)∣x2+y2≥4,(x−2)2+y2≤4}

Answer 1

(a)

P = (–3/2,3) and Q = (3/2,3)

You asked about (b) a couple of days ago.