Final answer:
The expression x2 + y2 = 1 does not represent a circle, it denotes a cylinder in three-dimensional space as it includes all values for z.Therefore, it is false.
Step-by-step explanation:
The student's question asks whether the set (x,y,z)∈R3 represents a circle, and this is false since the set describes a cylinder in three-dimensional space, not a circle. A circle is a two-dimensional shape where all points are at an equal distance from a central point (i.e., the center of the circle) within a plane.
In contrast, the given equation, x2 + y2 = 1, with z being any real number (since it's not restricted by the equation), represents a surface where every cross-section parallel to the x-y plane is a circle with radius 1. Therefore, all points that satisfy this equation form a cylinder in three-dimensional space, extending infinitely along the z-axis.
Therefore, it is false.