A = (0, 1)2 = (0, 1) × (0, 1) = {(x, y) ∈ R × R | 0 < x < 1 and 0 < y < 1}
B = {(x, y) ∈ R × R | x2 + y2 < 1}.

(a) Prove that A ∩ B ̸= ∅.

(b) Prove that A is not a subset of B

(c) Prove that B is not a subset of A.