(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement,

A = {(x, y) belongsto R^2 : (x−2)^2 + (y + 1)^2 < 9},

B = {(x, y)belongs to R^2 : y − 2x < 2}.

Show that A is a proper subset of B.

3. The attempt at a solution

Now I know that (x−2)^2 + (y + 1)^2 is an equation of a circle with centre translated to (2to the right on x axis and 1 down on the y axis. since its <9 its the interior area of the circle excluding actual circumference of the circle.

and graph of y-2x<2 has intercept y=2 and x=-1 and slopes from first qudrant to the forth and all the area above is in the set ( I am not sure)- excluding the actual line itself. but I have no idea how to prove this any help would be appriciated.

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# Homework Help: Proving A is a proper subset of B

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