Consider the following subsets of R^2:

Question

A={(x,y)∈R^2 : x2 +y2 ≤9},
B={(x,y)∈R^2 : y≥2x+1},
C = {(x, y) ∈ R^2 : y ≥ (x + 1)2}.

Prove that C is a proper subset of B.

Answer 1

well, (x+1)^2 = x^2+2x+1 ≥ 2x+1
That is, all elements of C are in B