The discussion revolves around verifying that the set W, defined as functions f in F(ℝ) satisfying f(-x) = f(x), is a subspace of F(ℝ). Participants confirm that the zero function is in W and discuss closure under addition, demonstrating that (f+g)(x) = (f+g)(-x). The main confusion arises around verifying closure under scalar multiplication, with clarification needed on the definitions of vector spaces and zero vectors. Emphasis is placed on understanding the definitions and properties of functions within the context of vector spaces. The conversation highlights the importance of grasping foundational concepts in linear algebra to solve such problems effectively.