Question 20
Consider the sets
$$
A = \{(x, y) \mid x, y \in \mathbb{R} \text{ and } x + y + 1 = 0\}
$$
and
$$
B = \{(x, y) \mid x, y \in \mathbb{R} \text{ and } x^3 + y^3 + 1 = 3xy\}.
$$
a) Show that $A \subset B$.
b) Prove that the set $B \setminus A$ has exactly one element.
$$
A = \{(x, y) \mid x, y \in \mathbb{R} \text{ and } x + y + 1 = 0\}
$$
and
$$
B = \{(x, y) \mid x, y \in \mathbb{R} \text{ and } x^3 + y^3 + 1 = 3xy\}.
$$
a) Show that $A \subset B$.
b) Prove that the set $B \setminus A$ has exactly one element.