The sentence "Set C is the set of all points in the circle defined by $x^2 + y^2 = 1$" can be expressed using set notation as:

$C = \{ (x, y) \in \mathbb{R}^2 \mid x^2 + y^2 = 1 \}$

This notation means that $C$ is the set of all ordered pairs $(x, y)$ in the real plane $\mathbb{R}^2$ such that $x^2 + y^2 = 1$, which is the equation of a circle with radius 1 centered at the origin.

Would you like further clarification or details?

Here are 5 related questions to expand your understanding:

1. How would you define the set for a circle with radius $r$ centered at the point $(h, k)$?
2. What is the parametric form of the circle $x^2 + y^2 = 1$?
3. How would you express the interior of the circle $x^2 + y^2 = 1$ using set notation?
4. Can the equation $x^2 + y^2 = 1$ be interpreted as a function? Why or why not?
5. How would you describe the set of points outside the circle in set notation?

Tip: Always check whether the set includes boundary points (like in this case) or if it only refers to an interior or exterior region.